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Question 517165: x^-75=0. Im having a hard time with this problem please help solve
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
I'm presuming you mean:
(Note: ^ does NOT mean "squared", it means "raised to the power of" the expression following the ^. If you meant  as I suspect, then you needed to have written x^2 - 75 = 0)
This is nothing more than the difference of two squares. But 75 is not a perfect square, you complain. Well, yes it is, sort of. It is the perfect square of  , right?
So re-write the equation:
^2\ =\ 0)
Or better yet, recognize that  and then write:
^2\ =\ 0)
Then follow the conjugate factors of the difference of two squares pattern, i.e. (a\ -\ b)) , to factor your LHS:
\left(x\ -\ 5\sqrt{5}\right)\ =\ 0)
And then just apply the Zero Product Rule.
John
My calculator said it, I believe it, that settles it
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