The equation that breaks the rule of Mathematics ! | Can you solve ?

Hinzugefügt: 2026-05-09

[00:00:00]Hello, welcome back once again.

[00:00:03]Today, we have this interesting radical equation problem.

[00:00:07]The square root of the quantity 5x - 4 is equal to -6.

[00:00:12]In this video, we're going to find the value of x that will satisfy this equation, if possible.

[00:00:18]Now, let us take note of the following.

[00:00:22]For real x, right?

[00:00:25]We have that the square root of x is greater than or equal to zero, right?

[00:00:31]But here, remember we're solving for the real value x.

[00:00:34]And we have that the square root of this quantity here is negative. So, it shows that this is out of this domain, right?

[00:00:42]So, we can conclude from this that there is no solution, right?

[00:00:48]There's no solution.

[00:00:51]Okay, awesome.

[00:00:53]But [snorts] what happens when we square both sides of this equation?

[00:00:56]Okay, so let's try that.

[00:00:59]If you square both sides to get the square root of 5x - 4 whole squared is equal to -6 whole squared.

[00:01:11]From here, this square gets cancelled with the square root.

[00:01:14]Then, we have 5x - 4 is equal to -6 squared will give us positive 36. Awesome.

[00:01:23]Now, we add 4 to both sides of the equation to get 5x - 4 + 4 is equal to 36 + 4.

[00:01:34]From here, we get 5x is equal to 40, right? So, divide both sides by 5.

[00:01:44]Here, this cancel. We get x is equal to 8.

[00:01:49]So, with this squaring of both sides we have a solution.

[00:01:55]But I want to let you guys know something. Sometimes squaring both sides of an equation will break in an external solution. For example, we have that X is equal to 2. If we square both sides, we get X squared is equal to 2 squared, which is 4. If you now try to solve for X here, we now have X is equal to -2 or X is equal to +2. But the original solution here is 2. So, you see, with the means of squaring both sides, we now have external solution in this case.

[00:02:25]So, this may be external solution. But let us find out if this will satisfy the given equation. For the left-hand side, we have that the square root of 5x -4 must be equal to -6. So, when X = 8, we get the square root of 5 * 8 -4 is equal to the square root of 5 * 8 is 40 -4. This is equal to the square root of 36, which is equal to +6.

[00:02:55]But the +6 is not equal to the left-hand side, which is -6.

[00:03:01]So, this is not a solution. It is extraneous, right? So, don't be surprised. Square root of 36 is just the principal square root.

[00:03:11]So, it should not be -6.

[00:03:14]So, that's why this falls out of the solution.

[00:03:18]Therefore, what should be our conclusion? Our conclusion is that there's no solution.

[00:03:23]Both real and complex.

[00:03:26]No solution.

[00:03:28]Both real and Both real and complex.

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