If $2 l - 3 m = - 1$ and $l m = 20$ , then the value of $4 l^{2} + 9 m^{2}$ is ________.

239

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240

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241

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361

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Solution

The correct option is B $241$

We know the identity $a^{2} + b^{2} - 2 a b = (a - b)^{2}$
Given, $2 l - 3 m = - 1$
Squaring on both sides, we get
$(2 l - 3 m)^{2} = (- 1)^{2}$
$\Rightarrow 4 l^{2} + 9 m^{2} - 12 l m = 1$ .....Also given that $l m = 20$
$\Rightarrow 4 l^{2} + 9 m^{2} - 12 \times 20 = 1$
$\Rightarrow 4 l^{2} + 9 m^{2} - 240 = 1$
$\Rightarrow 4 l^{2} + 9 m^{2} = 241$
Hence, option C is correct.

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