Solve for x, If \(\frac{\frac{2}{x}}{\frac{1}{p^2} + \frac{1}{q^2}}\) = m
A
\(\frac{4pq}{m(p + q)}\)
B
\(\frac{2p^2q^2}{m(q^2 + p^2)}\)
C
\(\frac{2pq}{m(q^2 + p^2)}\)
D
\(\frac{2p^2q^2}{m(p^2)}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{1}{p^2}\) + \(\frac{1}{q^2}\) = \(\frac{q^2 + p^2}{p^2 + q^2}\)
\(\frac{\frac{2}{x}}{\frac{p^2 + q^2}{p^2 q^2}}\)
m = \(\frac{2p^2q^2}{x(p^2 + q^2)}\)
= 2p2q2 = mx(p2 + q2)
x = \(\frac{2p^2q^2}{m(q^2 + p^2)}\)
Source: Myschool Past Questions Archive (Record #32505)