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

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Go from here.

If , then , of course.

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. :)

Quote:

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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

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If is odd, this is true, at least for real solutions.