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Make K the subject of the relation T = \(\sqrt{\frac{TK - H}{K - H}}\)

Mathematics
WAEC 2015

Make K the subject of the relation T = \(\sqrt{\frac{TK - H}{K - H}}\)
  • A. K = \(\frac{H(T^2 - 1)}{T^2 - T}\)
  • B. K = \(\frac{HT}{(T - 1)^2}\)
  • C. K = \(\frac{H(T^2 + 1)}{T}\)
  • D. K = \(\frac{H(T - 1)}{T}\)
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Correct Answer: Option A
Explanation
T = \(\sqrt{\frac{TK - H}{K - H}}\)

Taking the square of both sides, give

T2 = \(\frac{TK - H}{K - H}\)

T2(K - H) = TK - H

T2K - T2H = TK - H

T2K - TK = T2H - H

K(T2 - T) = H(T2 - 1)

K = \(\frac{H(T^2 - 1)}{T^2 - T}\)

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