Set of solutions of the equation 3- x -92 x -1-6- x 2-10 x -9-0 isA- 1-7-9B- 1-7-9-11C- 1-9-11D- 1-9

The correct option is B {1,7,9,11}3|(x − 9)^2(x − 1)|−6|x^2 − 10x + 9| = 0 ⇒3|x − 9||x − 9||x − 1| − 6 |x − 9||x − 1| = 0 nbsp; ⇒(3|x − 9| − 6) (|x − 9||x − ...

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Standard XII

Mathematics

Absolute Value Function

Set of soluti...

Question

Set of solutions of the equation $3 ∣ ∣ (x - 9)^{2} (x - 1) ∣ ∣ - 6 ∣ ∣ x^{2} - 10 x + 9 ∣ ∣ = 0$ is

{1, 7, 9}

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{1, 7, 9, 11}

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{1, 9, 11}

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{1, 9}

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Solution

The correct option is B ${1, 7, 9, 11}$
$3 ∣ ∣ (x - 9)^{2} (x - 1) ∣ ∣ - 6 ∣ ∣ x^{2} - 10 x + 9 ∣ ∣ = 0 \Rightarrow 3 | x - 9 | | x - 9 | | x - 1 | - 6 | x - 9 | | x - 1 | = 0 \Rightarrow (3 | x - 9 | - 6) (| x - 9 | | x - 1 |) = 0$
$\Rightarrow 3 | x - 9 | - 6 = 0 or | x - 9 | = 0 or | x - 1 | = 0 \Rightarrow x = 11, 7 or x = 9 or x = 1$
So, the solution set is ${1, 7, 9, 11}$

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The solution set of the equation $x^{l o g_{x} (1 - x)^{2}} = 9$ is

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Set of solutions of the equation 3∣∣(x−9)2(x−1)∣∣−6∣∣x2−10x+9∣∣=0 is

The correct option is B {1,7,9,11}3∣∣(x−9)2(x−1)∣∣−6∣∣x2−10x+9∣∣=0⇒3|x−9||x−9||x−1|−6|x−9||x−1|=0⇒(3|x−9|−6)(|x−9||x−1|)=0 ⇒3|x−9|−6=0 or |x−9|=0 or |x−1|=0⇒x=11,7 or x=9 or x=1 So, the solution set is {1,7,9,11}

Set of solutions of the equation $3 ∣ ∣ (x - 9)^{2} (x - 1) ∣ ∣ - 6 ∣ ∣ x^{2} - 10 x + 9 ∣ ∣ = 0$ is