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Solve for x, If \(\frac{\frac{2}{x}}{\frac{1}{p^2} + \frac{1}{q^2}}\) = m

Mathematics
JAMB 1982

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. \(\frac{2p^2q^2}{m(p^2)}\)
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Correct Answer: Option B
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 = \(\frac{2p^2q^2}{m(q^2 + p^2)}\)


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