If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

**viccal** · August 12th 2012, 01:13 AM

If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

Sorry, I haven't gotten used to LaTex yet, so I'll be posting an image again:

$If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?-math-prob-2.png$

My answer is 100, but the book says 98. How do you solve this?

Thank you!

**Prove It** · August 12th 2012, 01:16 AM

Originally Posted by viccal

If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

Sorry, I haven't gotten used to LaTex yet, so I'll be posting an image again:

$Click image for larger version. Name: math prob 2.png Views: 5 Size: 2.7 KB ID: 24495$

My answer is 100, but the book says 98. How do you solve this?

Thank you!

$\displaystyle \begin{align*} 4x + \frac{4}{x} &= 40 \\ x + \frac{1}{x} &= 10 \\ \left(x + \frac{1}{x}\right)^2 &= 10^2 \\ x^2 + 2 + \frac{1}{x^2} &= 100 \\ x^2 + \frac{1}{x^2} &= 98 \end{align*}$

**viccal** · August 12th 2012, 01:35 AM

Oh, wow! Thanks a lot! I didn't realize how careless I was in solving it. Thanks!

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