JAMB - Mathematics (1982 - No. 19)
Solve for x, If \(\frac{\frac{2}{x}}{\frac{1}{p^2} + \frac{1}{q^2}}\) = m
\(\frac{4pq}{m(p + q)}\)
\(\frac{2p^2q^2}{m(q^2 + p^2)}\)
\(\frac{2pq}{m(q^2 + p^2)}\)
\(\frac{2p^2q^2}{m(p^2)}\)
Explanation
\(\frac{1}{p^2}\) + \(\frac{1}{q^2}\) = \(\frac{q^2 + p^2}{p^2 + q^2}\)
\(\frac{\frac{2}{x}}{\frac{p^2 + q^2}{p^2 q^2}}\)
m = \(\frac{2p^2q^2}{x(p^2 + q^2)}\)
= 2p2q2 = mx(p2 + q2)
x = \(\frac{2p^2q^2}{m(q^2 + p^2)}\)
\(\frac{\frac{2}{x}}{\frac{p^2 + q^2}{p^2 q^2}}\)
m = \(\frac{2p^2q^2}{x(p^2 + q^2)}\)
= 2p2q2 = mx(p2 + q2)
x = \(\frac{2p^2q^2}{m(q^2 + p^2)}\)
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