# Thread: textbook isn't helping me with this problem can anybody help

1. ## textbook isn't helping me with this problem can anybody help

^5 square root of 5x-5 = ^5 square root of 6x-7

the ^ 5 is the little 5 on top before the square root symbol. I'm having trouble finding out how to solve for x

2. $\displaystyle \sqrt[5]{5x-5} = \sqrt[5]{6x - 7}$

$\displaystyle (\sqrt[5]{5x-5})^5 = (\sqrt[5]{6x-7})^5$

$\displaystyle 5x-5=6x-7$.

Go from here.

3. If $x^n = y^n$, then $x = y$, of course.

4. x^n = y^n sometimes has more solutions than just x = y.
Simplest example: x^2 = y^2 could be x = -y

Also, when raising to a power, we may actually have fewer solutions:
Consider sqrt(x) = -sqrt(y), squaring both sides gives x = y, but
sqrt(x) = -sqrt(x) is only true when x=0.
It is always a good idea to plug solutions back into the original equation to check.

For this problem, all solutions check out.

5. Originally Posted by snowtea
x^n = y^n sometimes has more solutions than just x = y.

Simplest example: x^2 = y^2 could be x = -y
If $\displaystyle n$ is odd, this is true, at least for real solutions.