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9^x + 9^-x = 62, what is 3^x + 3^-x

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by Ian Stewart » Mon May 25, 2009 8:24 pm
9^x + 9^-x = 62, what is 3^x + 3^-x

You might notice here that 9^x is equal to (3^x)^2, and that 9^(-x) = (3^(-x))^2. So if we raise 3^x + 3^-x to the power 2, we'll get something resembling, but not quite equal to, 9^x + 9^-x, but at least this will let us use the equation given:

(3^x + 3^-x)^2 = (3^x)^2 + 2*(3^x)(3^-x) + (3^-x)^2
= 9^x + 2*3^0 + 9^-x
= 9^x + 9^-x + 2
= 62 + 2
= 64

So 3^x + 3^-x is the square root of 64, or 8.
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Re: 9^x + 9^-x = 62, what is 3^x + 3^-x

by Brent@GMATPrepNow » Mon May 25, 2009 8:41 pm
ShakeM wrote:Subject says it all, can't seem to figure it out?
Nice question - where did you find it?

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