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

• October 23rd 2010, 10:01 AM
JessicaM
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.

(Thinking)

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

Jessica
• October 23rd 2010, 10:03 AM
Unknown008
Find:

$(p+q)^2$ first.

Then, it'll be easier.
• October 23rd 2010, 10:06 AM
Sambit
$\frac{1}{p^2} + \frac{1}{q^2} = \frac{p^2 + q^2}{p^2q^2}$
now the numerator can be written as $(p+q)^2 - 2pq$ and the denominator is $(pq)^2$

after this you should be able to do this by yourself.
• October 23rd 2010, 10:09 AM
JessicaM
but isnt (p+q)2 : p(squared)+ 2pq + q(squared) ? :S
• October 23rd 2010, 10:10 AM
JessicaM
Quote:

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

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

Thank you, helped alot. :D