$\begin{array}{1 1} 2 \\ 4 \\ 6 \\ 8 \end{array}$

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Answer : (b) 4

$Explanation: Let\;the\;two\;roots\;of\;the\;quadratic\;equation\;be\;\alpha\;\xi\;\beta$

$\alpha+\beta=\large\frac{4+\sqrt5}{5+\sqrt2}$

$\alpha\;\beta=\large\frac{8+2\sqrt5}{5+\sqrt2}$

$HM=\large\frac{2\alpha\beta}{\alpha+\beta}$

$=\large\frac{2(8+2\sqrt5)}{4+\sqrt5}$

$=\large\frac{4(4+\sqrt5)}{4+\sqrt5}=4.$

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