Number of solution(s) satisfying the equation, $3 x^{2} - 2 x^{3} = {log}_{2} (x^{2} + 1) - {log}_{2} x$ is:

1

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2

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3

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none of these

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Solution

The correct option is A $1$
$3 x^{2} - 2 x^{3} = l o g_{2} (x^{2} + 1) - l o g_{2} x$
$3 x^{2} - 2 x^{3} = l o g_{2} (\frac{x^{2} + 1}{x})$
$\Rightarrow 2^{3 x^{2} - 2 x^{3}} = \frac{x^{2} + 1}{x}$
Only $x = 1$ ,satisfies this equation.
Hence, number of solutions for the given equation is $1$ .

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