Number of real solutions of the equation $x^{4} + 8 x^{2} + 16 = 4 x^{2} - 12 x + 9$ is equal to

1

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2

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3

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4

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Solution

The correct option is A $1$
We need to find number of solution(s) of $x^{4} + 8 x^{2} + 16 = 4 x^{2} - 12 x + 9$
$\Rightarrow (x^{2} + 4)^{2} = (2 x - 3)^{2}$
$\Rightarrow x^{2} + 4 = \pm (2 x - 3)$
$\Rightarrow x^{2} + 2 x + 1 = 0$ or $x^{2} - 2 x + 7 = 0$
$\Rightarrow (x + 1)^{2} = 0$ or no solution .
$\Rightarrow x = - 1$
Hence, given equation have only one solution .

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