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

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ShakeM: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu May 21, 2009 9:57 pm

by ShakeM » Mon May 25, 2009 9:45 am

Subject says it all, can't seem to figure it out?

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Source: Beat The GMAT — Problem Solving | Mon May 25, 2009 9:45 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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?

Brent Hanneson - Creator of GMATPrepNow.com

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