anonymous
  • anonymous
Simplify: If x+x^-1=4 then what is (x^2+x^-2)/(x+x^-1)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I've tried this multiple times but I always end up getting 1=4. What am I doing wrong?!?
amriju
  • amriju
so...x+1/x=4..so simplifying..x^2-4x+1=0...right?...solve for x...x=2+3^1/2..and 2-3^1/2...so find the value now...
amriju
  • amriju
OR...(x^2+1/X^2)=(x+1/x)^2 -2...isn't it...so u have the value for x+1/x..don't u??

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More answers

anonymous
  • anonymous
The question basically relies on your ability to recognise that the numerator is simply the square of x + x^-1 minus 2. This you can arrive at using the idea behind 'Complete the square' which allows you to re-write x^2 + x^(-2) as [x + x^(-1)]^2 - 2. Hence the problem now can be re-written as: [x^2 + x^(-2)] [x + x^(-1)]^2 - 2 [4]^2 - 2 ------------- = ---------------- = -------- = ????? [x + x^(-1)] [x + x^(-1)] 4
anonymous
  • anonymous
@c0llege-g!rl
anonymous
  • anonymous
so would it be 9/2???
anonymous
  • anonymous
@genius12
anonymous
  • anonymous
nope you got the numerator wrong =P @c0llege-g!rl
anonymous
  • anonymous
oops! Meant 7/2 @genius12 Thanks so much for your help!
anonymous
  • anonymous
good job.

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