 Hello, can you guys hear me now? Okay, there was some problem with Google hangouts. Should I start? Okay Now I'm writing few questions on the board Please try to solve it one question is if X is equal to one divided by two minus root three then Find the value of x cube minus 2x square minus 7x Plus five Just solve it quickly. Have you done it? Okay one answer. I'm getting us three anyone else who has done it Okay, I'll give you a hint The hint is first rationalize it So X is equal to One by two minus root three. This is two plus root three Divided by two plus root three So you get in numerator two plus root three divided by two square is four Minus root three square is three So you get two plus root three So X is equal to two plus root three now try solving it Try to find out Q or something. Just see what happens You can do one thing. You can find out X minus two square first X minus two square would be root three square. So it would be X square plus 4x minus four is Equal to three So X square plus 4x It comes out to be equal to seven or you can write X square plus 4x Minus seven equal to zero, but how will it help you out? That you need to find out from here. So I found out square you find out X minus two cube X minus two cube and then try to find out something and you know that I'm trying to say That I have to find out X cube also and I have to find out This complete thing. So suppose let's take only one part. I have taken X minus two square and And now I am finding out X minus two cube. So X minus two cube would be a cube minus b cube minus three a b a minus b So it would be X cube minus 8 minus 2x square plus 4x now try to understand I Have X cube minus 2x square here what I need more So try to understand it is plus 4x and minus 8 So X cube what I do in this question is rather than finding this I can find this also, but this is not helping me out so What I do is I will Make cube of it. So this comes out to be eight plus three eleven Plus one second. I have made some mistake. I'll do this question one second How to solve this question job now look at here On the board to find out the value of X cube Minus 2x square minus seven X Minus five so I found out value as X is equal to two plus root three Now what I will do is that I'll find out X minus two cubes So I am taking this two on the other side X minus two cube is root three Cube so this comes out to be X cube minus eight Minus three AB so minus six X X minus two So this comes out to be X cube minus eight Minus six X square plus 12 X So this is nothing but X cube minus six X square Plus 12 X minus eight So instead of 2x square, I'm getting and this is how much this is three root three Now what I'm getting instead of 2x X cube minus 2x square. I am getting X cube minus 6x square So what I'll do is I'll find out X minus two square Which is equal to root three square So this gives me X square minus 4x Plus four that is equal to three. So this gives me X square minus 4x Plus one is equal to zero now. What I'll do. I'll subtract I'll multiply this with four So this becomes 4x square minus 16 X Plus four is equal to zero And I'll add it. So when I add it So this gives me plus 4x square minus 16 X Plus Four is equal to zero. So I get X cube Minus 2x square minus 4x Minus four is equal to zero now. What I have to do I have to make it minus seven X So it means that sorry, this is not zero. This is three root three It means that I have to subtract minus three X more from here So X is equal to two plus root three. So three X would be equal to six Plus three root three. So when I subtract it, so I subtract minus three X here I subtract minus three X here and here I subtract minus six Minus three root three. So what I get I get X cube minus 2x square minus seven X minus four is Equal to minus six because this root three and this root three is gone But I need minus five here So it means that I need to subtract minus one more here and minus one more here So I get minus seven as the answer Did it did you guys understand it One second it is one second one second guide. It is plus five. I have written here minus five So answer would be something else. Please don't worry. I'm changing it. This is plus five and here I have one second. This is plus five. So guys understand to make it plus five I need to add plus nine here. So I'll add plus nine here and Plus nine here also. So this is minus six plus nine is equal to Three so answer would be three in this case Did you guys understand? Yes, the answer is three. I wrote it wrong Did you understand? Okay, other questions. I hope you guys have copied. I am writing it on the find the value of Next question that you need to solve is Yes, few people are stingy copying. So I am turning the page How many of you have got the answer of this question? root five under root five plus two root six Okay, try to understand this type of question is solved with this method either If I have Something like this x plus y root z It is only possible in two cases either It can be square of a plus root B's So which is a square plus B plus a root B or It can be square of root a plus root B Which is a plus B plus root AB Now if you look at this question So it is five plus two root six. I Try to match it with a square plus B plus to a root B so here To root six is equal to two a root B Now two to gone a comes out to be one and B comes out to be six But when I find out the value of a square B value of a square plus B would be equal to One a square is one one square is one plus six seven and here what I am getting five It means that this particular method is not correct for this question So I'll move to the another part where I have root a plus root B whole square So what I do is that you look at here. I Have two root six is Is equal to two root AB So two to gone Root a B is equal to six or AB is equal to six Now there are different possibilities. I'm writing here. There are different possibilities AB is equal to six when a is equal to one and B is equal to six Then also AB is equal to six, but in that case a plus B would be seven, which is not my criteria So this I can't take now a is equal to two and B is equal to three And when in this case, I take a plus B. I get the answer as five So it means that the answer is a root two plus root three whole square So this can be written as Under root two plus under root three Whole square and this under root will come out if I write root three will plus root three So that is how you have to solve this question Did you guys understand it? always look at this Here root is only possible when you have one root or two root in the square So as soon as I look at this one root, I know that it is one of the two possibilities whether There is one root in the square or both of them are roots in the square So I try it with both the methods. So I first I take one root a plus root B And that square would be a square plus B plus two a root B So I match this to a root B because this root is coming Only one time it has to be equivalent to this from here a comes out to be six and one and B comes out to be six a square plus B comes out to be seven but here a square plus B is five So this cannot be my answer now I go to the second one where both of them are roots So a plus B plus two a root B. So a baby is equal to six here Now what I get is when I put a equal to one and B is equal to six a plus B comes out to be seven and When I put a is equal to two and B is equal to three a plus B comes out to be five and a into B is six So I understand that a is Two and B is three. I put it here. This becomes root two plus root three square is five plus two root six I replace five plus two root six with root two plus root three whole square the outcome is root two plus root three Sanjala you can post me the Question so this is how you have to solve this question Shraddha, did you understand now? I'm giving that question Shraddha wait Find X if log five Plus log five X plus one Minus log X plus five is equal to One what's the answer? Okay, then I'll wait for other answers Sanjana you post me that question I'll solve it Okay, let me solve this question. This is nothing but log five into five X plus one Divided by X plus five is equal to one So When do you get one log ten is equal to one? So this is nothing but log ten so it means that five X plus one divided by X plus five is equal to Ten so this gives me two five X plus one is equal to two X plus ten Three X is equal to nine X is equal to three Those who have solved this this is the question X is equal to Cube root two plus root three What is the value of X cube plus one by X cube? So this is nothing but X cube is equal to two plus root three as simple as that So this is two plus root three And this is one by two plus root three. I just rationalized one by two plus root three This will be two plus root three and when you rationalize it, it will be two minus root three in the numerator So root three root three one this comes out to be four Okay, next question find out What's the answer guys? Okay Okay, should I solve I have got answer only from Tane I'm waiting for one or two more answer Give me one or two more answers and I'll start solving So in this question always take out five to the power n common So I take out five to the power n common from numerator. There are two more fives left out here So I will have five square here Here n plus one is there if I take out one one five would be left out So that becomes six into five Divided by here. I take five to the power n nothing else left out So I have 13 minus two in two out of n plus one n is taken out So one five is left out. So this and this gone. This is 25 Minus 30 divided by 13 Minus 10 so this is nothing but minus five divided by three. This is your answer Okay, next question that you need to solve seven plus root five divided by seven minus root five Minus Seven minus root five divided by seven plus root five is equal to a plus Seven root five by 11 with the Find out a and b done Give me the answer guys too much of time Okay, not a very difficult question. I'll solve it part by part So look at here. So this is I'm solving this part first this this part seven plus root five divided by seven minus root five Multiplied with seven plus root five Here So what do I get? I get seven square 49 plus Five square is root five square is five plus 14 root five divided by two So this is nothing but 54 plus 14 root five divided by two which is equal to 27 plus seven root five Now let me solve this for you guys this is seven minus root five divided by seven plus root five and I multiply it with seven minus root five So what do I get guys? I made a mistake one second This is not we to this will be 49 minus five so one second as Usual calculation mistake. So this will be 49 Minus five which is equal to 44 so this will be 27 plus 2 root 5 divided by 22 And this will be how much this will be 49 plus 5 minus 14 root 5 divided by 44 So which is 54 minus 14 root 5 divided by 44 which is 27 minus 7 root 5 7 divided by 22 when you subtract it So this is 27 by 22 Plus 7 root 5 by 22 Minus this one is 27 by 22 minus 7 by 22 root 5 Which is nothing but This and this will be gone and this comes 14 5 divided by 22 So this comes out to be 7 root 5 divided by 11 So it means that there is no a here So a is equal to 0 and you see everything before B is coming out as it is here So B would be equal to 1. That's your answer That is how you have to solve this question I'm leaving it for one minute so that you can copy it and Then I'll start writing the next question Okay, next question guys So next question is the root 2 is equal to 1.4142 Then find the value of 2 minus 1 divided by root 2 plus 1 What's the answer? Give me the answer Post it Okay, try to understand all of you. What I'll do is first I'll rationalize it. So This is root 2 minus 1 I'll multiply it with the root 2 minus 1 And I'll multiply the denominator also with the root 2 minus 1 So what comes out is a root 2 minus 1 because this becomes root 2 plus 1 root 2 minus 1 is 2 minus 1 Which is 1 so denominator is 1 numerator is a root 2 minus 1 whole square Whole square. So what comes out is root 2 minus 1 and root 2 is 1.4142 Minus 1 so this is nothing but 0.4142 is the answer Write the complete answer not 414. You have to write one more 2 now another question Find out the value of 3 minus root Shraddha is problem from your side. It's not problem from my side Everyone else is getting good quality. So perhaps you refresh it or join join once again Okay, so I told that in this kind of question. I have two options one option is a plus root b whole square So a plus root b whole square is a square plus b plus two root a b Or I have root a plus root b whole square, which is a plus b Plus Two a b two root a b. So this question first I'll solve with this method. So minus 2 root 2 is equal to 2 a root b So this and this gone a comes out to be equal to minus 1 and b comes out to be equal to 2 So I find out the value of a square plus b minus 1 square is 1 and b is 2 This is equal to 3. So I'm getting the same thing here. So this is nothing but minus 1 plus root 2 whole square So I with so I keep it here. This is nothing but root 2 under root root 2 minus 1 whole square So what will come outside root 2 minus 1 will come outside So that's the answer. Okay next question x is equal to Then find out the value of root x Minus 1 by root x Okay, one answer. I am getting as minus 2 Any other answer should I solve it? Okay, so guys, I just solved this question here. There was negative. So I will find out root x here root x would be root 3 plus 2 root 2 I just solve it with this method where a plus root b square is a square plus b plus 2 a root b I'll compare 2 a root b with 2 root 2 So I get a is equal to 1 and b is equal to 2 So a square plus b anyway comes out to be so this comes out to be root 2 plus 1 Whole square. So x would be root x would be equal to root 2 plus 1 So here I keep root 2 plus 1 minus root 2 plus 1 I just generalize it rationalize it. Sorry. So this will be root 2 minus 1. This will be root 2 minus 1 So this is root 2 plus 1 minus This will be root 2 minus 1 and root 2 minus 1 root 2 plus 1 is 2 minus 1 So this is root 2 minus 1 minus root 2 minus 1 because 2 minus 1 is 1. So this is root 2 Sorry, this is plus 1 Plus 1 minus root 2 minus minus plus 1 so root 2 root 2 gone plus 1 plus plus 1 is 2 So answer is 2 Now if anyone has any doubt, please send me the pictures I'll solve it Or let me know if you have doubt in any particular topic Write that topic in the comment box. I'll start solving questions from there Otherwise, I'll wrap up the class Okay guys, tell me if you have any doubt Post otherwise I'm done with most of the questions which I got from your view as doubt Okay, solve one more question. I have one more question left out. Give me the answer guys Okay, one answer I've got I'm waiting for a few more answers Root 8 is a wrong answer You have nothing to do here if if if this under root is this you find out square of of both side So a square of this side is 13 minus a root 10 Square of this side is 8 plus 5 plus 40 So which is nothing but 13 plus 2 root 40 Which can root 40 can be written as 4 into Root 4 into root 10 and root 4 would be 2 so this would be 13 plus 4 root 10 So this 13 and 13 matches with each other 10 and 10 matches with each other So minus a comes out to be equal to 4 a is equal to minus 4 That is what the answer is Did you get the answer? Did you understand the solution? Okay, so I'll give you two minutes to post any doubt if if there is no doubt then I'll wrap up the session Two more minutes If you have any doubt Okay, so nobody's asking any questions. So I'm wrapping up the session now