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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  a2+b2 is 

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a
150
b
153
c
156
d
159

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detailed solution

Correct option is B

A-G=3/2, G-H=6/5 We know that G2=AH →G2=32+G(G−6/5)⇒G=6,A=15/2⇒ab=36,a+b=15→a=12,b=3a2+b2=144+9=153


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