# Thread: If p+q=3 and pq=2, find 1/p^2 + 1/q^2.

1. ## If p+q=3 and pq=2, find 1/p^2 + 1/q^2.

Hi, i know this is probably a very simple problem to solve but i just cant figure it out.

Question: if p+q=3 and pq=2, find the value of 1/p(squared) + 1/q(squared) without finding the values of p and q.

If anyone could help me I would be very happy. Please let me know.

Jessica

2. Find:

$\displaystyle (p+q)^2$ first.

Then, it'll be easier.

3. $\displaystyle \frac{1}{p^2} + \frac{1}{q^2} = \frac{p^2 + q^2}{p^2q^2}$
now the numerator can be written as $\displaystyle (p+q)^2 - 2pq$ and the denominator is $\displaystyle (pq)^2$

after this you should be able to do this by yourself.

4. but isnt (p+q)2 : p(squared)+ 2pq + q(squared) ? :S

5. Originally Posted by Sambit
$\displaystyle \frac{1}{p^2} + \frac{1}{q^2} = \frac{p^2 + q^2}{p^2q^2}$
now the numerator can be written as $\displaystyle (p+q)^2 - 2pq$ and the denominator is $\displaystyle (pq)^2$

after this you should be able to do this by yourself.

Thank you, helped alot.