144 130, A, B, C are distinct posit...

144 130, A, B, C are distinct positive integers, less than or equal to 10. The arithmetic mean of A and B is 9. The GM of A and C is 6V2, then H.M of B and C is (A) 180/19 (B) 90/19 (C) 80/9 (D) 144/17 131. Let a, b, cbe in GP.Ifp is the AM. between a and b and a is the A.M. between band c, then bis equal to

JEE/Engineering Exams
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( A, B, C leqslant 10, quad triangle, B, C in I ) ( frac{A+B=9}{2} Rightarrow A+B=18 ) ( sqrt{A cdot C}=6 sqrt{2} Rightarrow A cdot C=72=9 times 8 ) ( therefore A=8, C=9, B=10 ) ( A A B B C=frac{2 B C}{B+C}=frac{2(10) 19)}{1210+98}=frac{180}{19} )
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