The harmonic mean of the roots of the equation (5 + sqrt(2))x^2 - (4 + sqrt(5))x + 8 + 2sqrt(5) = 0 is

The harmonic mean of the roots of the equation (5 + \... | Sequence & Series (Mathematics)

(b) : Let $\alpha, \beta$ are the roots of the given quadratic equation $\\$ Therefore $\alpha+\beta=\frac{4+\sqrt{5}}{5+\sqrt{2}}$ and $\alpha \beta=\frac{8+2 \sqrt{5}}{5+\sqrt{2}}\\1$ Let $H$ be the harmonic mean between $\alpha$ and $\beta$ $\\$ Then $H=\frac{2 \alpha \beta}{\alpha+\beta}=\frac{16+4 \sqrt{5}}{4+\sqrt{5}}=\frac{4(4+\sqrt{5})}{(4+\sqrt{5})}=4$

Explanation

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