A) 2
B) 4
C) 6
D) 8
Correct Answer: B
Solution :
Given equation is \[(5+\sqrt{2}){{x}^{2}}-(4+\sqrt{5})x+8+2\sqrt{5}=0\] Hence \[{{x}_{1}}+{{x}_{2}}=\frac{4+\sqrt{5}}{5+\sqrt{2}}\] and \[{{x}_{1}}{{x}_{2}}=\frac{8+2\sqrt{5}}{5+\sqrt{2}}=\frac{2(4+\sqrt{5})}{5+\sqrt{2}}=2({{x}_{1}}+{{x}_{2}})\] Harmonic mean\[=\frac{2{{x}_{1}}{{x}_{2}}}{{{x}_{1}}+{{x}_{2}}}=\frac{2{{x}_{1}}{{x}_{2}}}{{{x}_{1}}{{x}_{2}}/2}=4\].
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