Interesting algebraic equation | Can you solve ?

Added: 2026-05-12

[00:00:00]Hello, welcome back once again. Today we're going to solve this interesting equation. Root of x / x is equal to 8.

[00:00:09]In this video, we're going to find the value of x that will satisfy this equation. So, let's get started. Now, take a look at the left hand side. We have division by x. It clearly implies that x is not equal to zero also.

[00:00:26]Okay. Now I will be presenting two I mean three different methods. Okay. So let's start with our first method.

[00:00:42]So in our first method we're going to square both sides of the equation as it is. So here we have roo<unk> of x / x² this is equal to 8^ 2.

[00:00:59]So from here you know this is <unk>x 2 and that will give us x right. So we have x then divided by here this is x 2 that will give us x to the^ of 2. So this is equal to h 2 will give us 64 also. Now from here we know x / x^2 remember it will simplify to 1 /x right because the left hand side is same as x / x * x. So you can cancel out this x and this x leaving us with only 1 /x on the left hand side. So we have here 1 /x is = 64. So cross multiply from here to get 64x = 1. Divide both sid by 64 to get x is equal to 1 / 64.

[00:01:50]This is our correct answer. Let's see the second method.

[00:02:01]For the second method, we are going to first cross multiply. We have rootx / x which is equal to 8. Put it over one. Then cross multiply to get 8x is equal to square roo<unk> of x. Square both sides to eliminate this radical. We get 8x² is =<unk> of x squar.

[00:02:30]From here x 8 square is 64. x to the^ 2 we get 64x^2 is equal to roo<unk>x^2 square cancel square root giving us x take this x to the left hand side to get 64x^2 - x = 0 factor out x into bracket 64x - 1 is = 0 and we see it implies from here either x is equal to zero or 64x - 1 = 0. I want to both sign divide both side by 64 to get x = 1 / 64. So I think this method is longer, right? And we know this is not a solution. But here 1 / 64 is a valid solution.

[00:03:21]So no space for our third method. I think I'm going to put it down somewhere. Okay. So let's put it down somewhere here. So for final method that is the third one.

[00:03:37]So from left hand side we can write that as x ^ 1 / 2 / x ^ 1 which is equal to x. Then we use this this initial law a^ of m / a^ of n is equal to a to the mus n.

[00:03:58]So here on the left hand side it will be x to the 1 / 2 - 1 giving us -1 / 2. So this is equal to 8. Now to get rid of this we raise both side to the power of -2. Right? So raise both side to the power of -2.

[00:04:17]So 1 /2 * -2 will give us just positive 1. So we have x on the left hand side which is equal to remember this property a to the m is equal to 1 / a to the m.

[00:04:30]So this will be 1 / 8^ 2 giving us 1 / 64. So here is the third method. So I want to see at the comment section the one which is the best. Thank you for watching. If you enjoyed the video, please kindly subscribe to this channel.

[00:04:46]Also like, comment and share.