Number of real solutions of the equation $| x - 3 |^{3 x^{2} - 10 x + 3} = 1$ is

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 C $3$
$| x - 3 |^{3 x^{2} - 10 x + 3} = 1$
$case-1, | x - 3 | = 1$
$x - 3 = - 1 or x - 3 = 1$
$x = 2 or x = 4$

$case-2, 3 x^{2} - 10 x + 3 = 0$
$3 x^{2} - 9 x - x + 3 = 0$
$3 x (x - 3) - 1 (x - 3) = 0$
$(3 x - 1) (x - 3) = 0$
$x = 3, \frac{1}{3}$
but $x \neq 3$ as $0^{0}$ is not defined
Hence, $x = \frac{1}{3}, 2, 4$
Only three solutions are there

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Similar questions

Number of real solution(s) of the equation ${| x - 3 |}^{3 x^{2} - 10 x + 3} = 1$ is

| x - 3 |^{3 x^{2} - 10 x + 3} = 1

{(\frac{9}{10})}^{x} = - 3 + x - x^{2}

x^{2} - x + 3 + {(\frac{9}{10})}^{x} = 0

{(\frac{9}{10})}^{x} = - 3 + x - x^{2}

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