Number of real solutions of the equation - x -3-3 x 2-10 x -3-1 isA- 1B- 2C- 3D- 4

The correct option is C 3|x 3|^3x^2 10x+3=1 case 1, |x 3|=1 x 3= 1 nbsp; or x 3=1 x=2 nbsp; or x=4 case 2, 3x^2 10x+3=0 3x^2 9x x+3=0 3x(x 3) 1(x 3) ...

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Standard XII

Mathematics

Absolute Value Function

Number of rea...

Question

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

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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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Number of real solutions of the equation |x−3|3x2−10x+3=1 is

The correct option is C 3|x−3|3x2−10x+3=1 case-1, |x−3|=1 x−3=−1 or x−3=1 x=2 or x=4 case-2, 3x2−10x+3=0 3x2−9x−x+3=0 3x(x−3)−1(x−3)=0 (3x−1)(x−3)=0 x=3,13 but x≠3 as 00 is not defined Hence, x=13,2,4 Only three solutions are there

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