Solve for $y : 2 y^{2} + 4 = 9 y$

{2, 4}

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{\frac{1}{2}, 2}

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{2, 2}

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{\frac{1}{2}, 4}

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Solution

The correct option is D ${\frac{1}{2}, 4}$
Given equation is $2 y^{2} + 4 = 9 y$
$\Rightarrow 2 y^{2} - 9 y + 4 = 0$
$\Rightarrow 2 y^{2} - 8 y - y + 4 = 0$
$\Rightarrow 2 y (y - 4) - 1 (y - 4) = 0$
$\Rightarrow (y - 4) (2 y - 1) = 0$
$\Rightarrow y - 4 = 0$ or, $2 y - 1 = 0$
$\Rightarrow y = 4$ or $y = \frac{1}{2}$
Hence, option D is correct.

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