 Welcome friends. So continuing with our series on problem solving, let's try and solve this problem. So it's given that x squared plus 1 pi x squared is 27. This is the given information and basis this information, you have to find out what's the value of x plus 1 upon x and x minus 1 upon x. So let's start with the first one. So what is given? It's given that x squared plus 1 upon x squared is equal to 27. Now if you remember, we have seen such identity or such terms before and such terms were expressed in let's say a plus b whole square was there it is. So when it was a plus b whole square, it's a square plus 2 a b plus b square. Now if you see carefully, there is a power 2 here and in the final term, there is power 1 on x. Similarly, here it is 2 and then it has to be reduced to 1, right? So hence, if you see if we square the target here, that means what is the target? Target is x plus 1 upon x, right? If you square this term up here, what will you get? You will get x squared plus 2 times x times 1 by x plus 1 upon x whole square, isn't it? So if you see, this is nothing but x plus 1 upon x if I square and I am using this identity over here will be equal to what? x squared plus 2 plus 1 upon x squared, right? This x and this x can be cancelled, right? And ideally it should be given that x is not equal to 0. So assuming x is not equal to 0, you can cancel that, right? Now obviously x cannot be 0. Why if x is 0 then it cannot be equal to 27 here? This expression cannot be 27. So clearly you know that x is not equal to 0. So this cancellation is allowed. Why am I insisting upon ensuring that x is not equal to 0 is division by 0 is not defined in mathematics, okay? Now if you see, you get a term in the right hand side x square plus 1 upon x square plus 2, isn't it? I have just rearranged this right hand side here. Now if you see, x square plus 1 upon x square is already given. What's the value? The value is 27. It's given, right? So hence this total is 27 plus 2 and hence it is 29, right? So what do we observe? We see that x plus 1 upon x whole square is how much? 29. So I will do what? Square rooting both sides. Square rooting both sides. What will you get? You will get x plus 1 upon x is equal to plus or minus square root of 29. Why plus and minus? Because if you square these two terms here, if you square this, you should come back to here. So whether it is plus 20, root 29 or minus root 29, you will, squaring will get you 29. So square root. So you know whenever there's an equation, something like this where x square is let's say something like A, then x is nothing but plus minus root of A. So that's what we did. So we square root both sides and we get that and that was what was expected. So x plus 1 by x value is root over plus minus root over 29. Now let's get back to the second question. Second question is x minus 1 by x with the same given conditions. So the given condition is x square plus 1 upon x square is equal to 27. You have to find out what? x minus 1 by x. So if you square x minus 1 by x, what will you get? You will get x square minus 2 times x times 1 upon x plus 1 upon x whole square, isn't it? Squaring this will give you this much. Now that means what? This is nothing but x squared plus 1 upon x squared minus 2 because again x is not equal to 0. So this x can go. So this is the final result. But x square plus 1 by x square was given as to be 27. So 27 minus 2 is 25, isn't it? So that means x minus 1 by x whole square is 25. So square rooting both sides like what we did in the previous question will be plus or minus under root 25 which is nothing but plus or minus 5 because under root 25 is 5. So hence we see x minus 1 by x value is plus minus 5. So this is how you have to solve such problems. So what did we learn? We learned using algebraic identities for evaluating algebraic expressions. So keep this particular method in mind.