If-2a-1-2-a-Find-2a-2-a-2a-

Question Number 214247 by hardmath last updated on 02/Dec/24

If 2 a = 1 - 2 \sqrt{a}

Find \frac{{2 a}^{2} + \sqrt{a}}{2 a} = ?

Answered by A5T last updated on 02/Dec/24

2 a = 1 - 2 \sqrt{a} \Rightarrow {\begin{cases} \sqrt{a} = \frac{2 a - 1}{- 2} \\ {(2 a - 1)}^{2} = 4 a \Rightarrow 4 a^{2} + 1 = 8 a \end{cases}

\Rightarrow \frac{2 a^{2} + \sqrt{a}}{2 a} = \frac{2 a^{2} + \frac{2 a - 1}{- 2}}{2 a} = \frac{- 4 a^{2} + 2 a - 1}{- 4 a}

= \frac{- (4 a^{2} + 1) + 2 a}{- 4 a} = \frac{- 8 a + 2 a}{- 4 a} = \frac{3}{2}

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