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Mush · #2 January 6th, 2009, 11:32 PM

Quote:

Originally Posted by Chizum

I'm in calculus but there is a basic precalculus rule that I'm shady on and need to use.

If I had $y^2 = 3 - x$ and I wanted to solve for y, would I get y = +/- the square root of x - 3 ?

I forget if that is the proper situation when you have to use +/-

IF it is, then I need to set it equal to x - 1 and solve for x. How would that solve when the +/- is involved?

Yes. Whenever you have an equation of the form $y^2 = something$ , then y is ALWAYS given by $y = \pm \sqrt{something}$ .

This is because x^2 = (-x)^2, and hence if you were to do the inverse, you wouldn't know whether x or -x was the original term, so we include both as solutions!

This isn't just the rule, but in fact, it is the rule for any EVEN exponent.

So if you had $y^4, y^6, y^{2023424}, y^{99999999994}$ , then your answer would always be $\pm$ .

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