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Q.

The minimum value of $a^{2} - a b x - b^{2} x^{2}$ is

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a

$\frac{4 a}{5}$

b

$\frac{4 a^{2}}{5}$

c

$\frac{5 a}{4}$

d

$\frac{5 a^{2}}{4}$

answer is D.

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Detailed Solution

$a^{2} - a b x - b^{2} x^{2} \Rightarrow - b^{2} x^{2} - a b x + a^{2}$

$\frac{4 a c - b^{2}}{4 a} = \frac{4 (- b^{2}) (a^{2}) - {(a b)}^{2}}{4 - b^{2}}$

$= \frac{- 4 a^{2} b^{2} - a^{2} b^{2}}{- 4 b^{2}}$

$= \frac{- 5 a^{2} b^{2}}{- 4 b^{2}}$

$= \frac{5 a^{2}}{4}$

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