Which of the following is a possible value of $x$ , if $5 x^{2} - 10 x + 4 = 0$ ?

2 \sqrt{5}

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1 + 2 \sqrt{5}

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1 + \frac{\sqrt{5}}{5}

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2 + \frac{\sqrt{5}}{10}

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10 + \frac{\sqrt{5}}{10}

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Solution

The correct option is C $1 + \frac{\sqrt{5}}{5}$
Given expression is $5 x^{2} - 10 x + 4 = 0$

Solutions of the equation $a x^{2} + b x + c = 0$ are given be $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
Hence, solutions of the given equation are $\frac{10 \pm \sqrt{10^{2} - 4 (5) (4)}}{2 (5)}$

$= \frac{10 \pm \sqrt{100 - 80}}{10}$

$= 1 \pm \frac{\sqrt{5}}{5}$

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