Given that the value of $m$ is $- 3$ ,the solution set for the equation $\sqrt{m x - 5} = x + 3$ is:

{- 3, 3}

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{- 2}

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{- 2, - 7}

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{3, 6}

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Solution

The correct option is C ${- 2, - 7}$
Given, $\sqrt{m x - 5} = x + 3$
Squaring on both the sides, we get
$m x - 5 = (x + 3)^{2} \Rightarrow m x - 5 = x^{2} + 6 x + 9$
Put the value of $m = - 3$ , we get
$- 3 x - 5 = x^{2} + 6 x + 9$
$\Rightarrow x^{2} + 6 x + 9 + 3 x + 5 = 0$
$\Rightarrow x^{2} + 9 x + 14 = 0$
$\Rightarrow x^{2} + 7 x + 2 x + 14 = 0$
$\Rightarrow x (x + 7) + 2 (x + 7) = 0$
$\Rightarrow (x + 7) (x + 2) = 0$
Then $x = - 7$ and
$x = - 2$

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