JAMB - Mathematics (1989 - No. 13)
Make R the subject of the formula S = \(\sqrt{\frac{2R + T}{2RT}}\)
R = \(\frac{T}{(TS^2 + 1)}\)
R = \(\frac{T}{2(TS^2 - 1)}\)
R = \(\frac{T}{2(TS^2 + 1)}\)
R = \(\frac{R}{2(TS^2 + 1)}\)
Explication
S = \(\sqrt{\frac{2R + T}{2RT}}\)
Squaring both sides,
\(S^{2} = \frac{2R + T}{2RT}\)
\(S^{2} (2RT) = 2R + T\)
\(2S^{2} RT - 2R = T\)
\(R = \frac{T}{2TS^{2} - 2}\)
= \(\frac{T}{2(TS^2 - 1)}\)