The H.M. between two numbers is 16/5, their A.M. is A and G.M. is G. If 2A + G2 = 26 then the numbers are

The H.M. between two numbers is 16/5, their A.M. is A and G.M. is G. If $2 A + G^{2} = 26$ then the numbers are

$\begin{array}{l} \frac{2 a b}{a + b} = \frac{16}{5}, a + b + a b = 26 \\ \Rightarrow a + b = \frac{5}{8} a b, a + b + a b = 26 \end{array}$

$∴ \frac{13}{8} a b = 26 \Rightarrow a b = 16$ and $a + b = 10$

Thus, numbers are 2 and 8.

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