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Q.

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

answer is B.

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Detailed Solution

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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