Number of real solutions of the equation -x-3-3 x2-10 x-3-1 isA- 4B- 3C- 2D- 1

The correct option is B 3 | x 3 |^3x^2 10x+3 = 1 [x≠ 3] ⇒ | x 3 |=1 ⇒ x=2 or 4 is the solution If x 3 ≠ 0 then 3x^2 10x+3=0 is another solution 3x^2 10x+3=0 ...

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Standard XIII

Mathematics

Roots of a Quadratic Equation

Number of rea...

Question

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

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Solution

The correct option is B
3

${| x - 3 |}^{3 x^{2} - 10 x + 3} = 1$ [ $x \neq 3$ ]

$\Rightarrow | x - 3 | = 1$

$\Rightarrow x = 2$ or 4 is the solution

If $x - 3 \neq 0$ then $3 x^{2} - 10 x + 3 = 0$ is another solution

$3 x^{2} - 10 x + 3 = 0 \Rightarrow (3 x - 1) (x - 3) = 0$

$\Rightarrow x = 3$ or $x = \frac{1}{3}$ But $x \neq 3,$ so, $x = \frac{1}{3}$

Hence, the number of solutions is 3, i.e., $x = \frac{1}{3}, 2, 4$

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Number of real solution(s) of the equation |x−3|3x2−10x+3=1 is

The correct option is B 3 |x−3|3x2−10x+3=1 [x≠3] ⇒|x−3|=1 ⇒x=2 or 4 is the solution If x−3≠0 then 3x2−10x+3=0 is another solution 3x2−10x+3=0⇒(3x−1)(x−3)=0 ⇒x=3 or x=13 But x≠3, so, x=13 Hence, the number of solutions is 3, i.e.,x=13, 2, 4

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