 Okay, in this question, it's given that x square plus 1 by x square is 83, okay. And you have to find out the value of x cube minus 1 by x cube. I know many of you get confused the moment you see such kind of question, but trust me these are very mechanical in nature, you know what to do actually. So hence, if you see, they are playing with powers that means, you know, and powers of two terms, right? So if you see there are two terms, two terms and their power is given as, and power is 2, here the power is 3. And one important thing is x into 1 by x is a constant that is 1. If you see the two terms which are there x, and the variable here is 1 upon x, so multiplication is 1. So this kind of a problem are typical, okay. And they use nothing but algebraic identities, right? So if you see x square plus 1 by x square is given, that means you can find out x plus 1 by x from here, how? So let us say x square plus 1 by x is equal to 83, is it? Now if you see this 83 is closer to 81 which is 9 square, that itself is an indication that you reduce it to power, you know, square, some square. So hence, x square plus 1 by x square is can be written as 81 plus 2, isn't it? Now this 2, you take it on the left hand side, so that only square term, perfect square term stays in the right hand side. So minus 2 is 81, which is equal to 9 square, isn't it? Now if you see closely this one, this is algebraic identity, right? How? It is x square plus 1 by x square minus 2 times x times 1 by x, isn't it? See, x into 1 by x was 1 and 2 can be expressed like this and which helps us in completing the square. How? So if you see this is nothing but x minus 1 by x whole square's expansion was this, right? Is equal to 9 square. Wow, this is so good. So hence, if you see, I can find out x minus 1 by x will be nothing but plus 9 or minus 9, both. Both could be, you know, the value, isn't it? Both could be the value. So x minus 1 by x is plus 9 or minus 9. So now what is the next step? The question was to find out x cube minus 1 by x cube. So if you know, we know this identity. What was that identity? x cube minus 1 by x cube is this, isn't it? x cube minus 1 by x cube. So basically, a cube minus b cube identity was given as a minus b whole cube, right? Minus 3ab or rather plus 3ab times a minus b. This was one identity. Another identity which we know is a cube minus b cube is a cube. Sorry, this is a minus b times a square plus a b and then plus b square, right? You can use whichever, either of the two. So let us say x cube minus 1 by cube will be equal to nothing but x minus 1 by cube. Let us use this particular identity. Is nothing but x square plus x into 1 by x plus 1 by x square, isn't it? Now x minus 1 by x is given plus 9. So let us take plus 9 first. So when x minus 1 by x is equal to plus 9. So what will happen? It will be 9 into an x square plus 1 by x square. Was it given? Yes. It was given to be equal to 83. See, right? So hence, I can write 83 plus x into 1 by x is 1 simply, right? So hence, it is 9 into 84. 9 into 84, isn't it? And the value would be 9, 4, or 36 carry 3. 9 is 72 plus 3, 756. So this is the value. If x minus 1 by x is minus 9, then what will happen? Then again, nothing will happen. Only the sign will change here, right? This will become simply minus 9 and everything will remain the same. But usually, we take the x cube minus 1 by cube is either 756 or minus 756. Is it okay? So what is the learning in this question? The learning is that if you see some expressions like these, then you know very far for sure that there has to be some use of algebraic identities. And if you play with the 2 and 3 algebraic identity, which is common, that is a plus b whole square or a minus a square minus b square or a plus b whole cube and the different corollaries or different types of identities which we have seen around these three, four basic identities. So be very clear. So whenever such problems are there, you have to use algebraic identities.