Germany | Can You Solve This? | A Nice Algebra Problem x=?

追加: 2026-05-14

[00:00:00]Hello everyone, you are welcome. Today we have a very interesting square root math question.

[00:00:07]Here is square root of x plus square root of x is equal to x. So I will try to find out the value of x. [snorts] So let's start our solution. So first of all we look at the left hand side here, the same expression square root of x is added two times.

[00:00:23]So therefore here we can write this left hand side and this is just two times square root of x is equal to x.

[00:00:35]And our target to find out the value of x, we will try to eliminate this square root from the x. So for that here we will take square on both sides. So let us take square on both sides.

[00:00:48]So this expression in the left hand side, this will become this will become two squared times square root of x whole square is equal to x squared.

[00:01:04]And this two squared it is just four.

[00:01:08]And here square and square root will be cancelled, so this will become only x is equal to x squared.

[00:01:16]And we take this expression to the right hand side.

[00:01:20]So this will become x squared minus four x.

[00:01:27]And this side will become zero.

[00:01:30]There is x common in both the terms, we will take out x common.

[00:01:35]So taking x common this will become x minus four is equal to zero.

[00:01:43]Here the product of these two expression is zero, so here either this x will be zero or this one expression will be zero.

[00:01:51]So from here we will get x is equal to zero or x minus 4 is equal to zero.

[00:02:01]And we will take this four to the right-hand side. It become x is equal to four.

[00:02:07]Here we get two real values of x. x is equal to zero and x is equal to four.

[00:02:15]Here we can verify these values of x that as x is equal to zero and x is equal to four are the exact and correct values of x or not.

[00:02:25]So, let's substitute these values one by one in the equation in the question.

[00:02:30]So, here we first we will try to sub- substitute x is equal to zero.

[00:02:35]So, let's verify x is equal to zero.

[00:02:38]So, this will become square root of zero plus square root of zero is equal to zero. The square root of zero is zero plus square root of zero is zero is equal to zero.

[00:02:53]And zero is equal to zero.

[00:02:56]So, here x is equal to zero verifying the equation the question.

[00:03:00]We will try to verify the second value of x that is x is equal to four.

[00:03:06]So, let's try to verify this one value of x.

[00:03:09]So, the original question will become that is square root of x is equal to square root of four plus square root of four is equal to that is four.

[00:03:20]And square root of four is just two.

[00:03:23]And this is also two is equal to four.

[00:03:27]Now, two plus two is simply four is equal to four.

[00:03:32]Again, both side are equals. It means that x is equal to zero and x is equal to four are the exact and correct solutions of this interesting square root algebra math question.