Question

Simplify: If x+x^-1=4 then what is (x^2+x^-2)/(x+x^-1)?

Answer 1

I've tried this multiple times but I always end up getting 1=4. What am I doing wrong?!?

Answer 2

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...

Answer 3

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??

Answer 4

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

Answer 5

@c0llege-g!rl

Answer 6

so would it be 9/2???

Answer 7

@genius12

Answer 8

nope you got the numerator wrong =P @c0llege-g!rl

Answer 9

oops! Meant 7/2 @genius12
Thanks so much for your help!

Answer 10

good job.