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

• Aug 12th 2012, 02:13 AM
viccal
If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?
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:

Attachment 24495

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

Thank you!
• Aug 12th 2012, 02:16 AM
Prove It
Re: If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?
Quote:

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:

Attachment 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*}
• Aug 12th 2012, 02:35 AM
viccal
Re: If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?
Oh, wow! Thanks a lot! I didn't realize how careless I was in solving it. Thanks!