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Consider two positive numbers a and b. If A.M. of a and b exceeds their G.M by 3/2 and G.M of a and b exceeds their H.M by 6/5 then the value of $a^{2} {+b}^{2}$ is

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150

153

159

156

answer is B.

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Detailed Solution

A-G=3/2, G-H=6/5

$\begin{array}{l} We know that G^{2} = AH \\ \to G^{2} = (\frac{3}{2} + G) (G - 6 / 5) \\ \Rightarrow G = 6, A = 15 / 2 \\ \Rightarrow ab = 36, a + b = 15 \\ \to a = 12, b = 3 \\ a^{2} + b^{2} = 144 + 9 = 153 \end{array}$

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