The sum of the solutions of the equation -x-2-x-x-4-2-0- x0 is equal to-

Case 1: When √(x)≥ 2 √(x) 2+x 4√(x)+2=0 ⇒ x 3√(x)=0 ⇒ x=0,x=9 As, √(x)≥ 2 ⇒ x=9 Case 2: When √(x) 2 2 √(x)+x 4√(x)+2=0 ⇒ x 5√(x)+4=0 ⇒ (√(x) 4)(√(x) 1)=0 ⇒ x=1 ...

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Standard XIII

Mathematics

Absolute Value Function

The sum of th...

Question

The sum of the solutions of the equation $| \sqrt{x} - 2 | + \sqrt{x} (\sqrt{x} - 4) + 2 = 0, (x > 0)$ is equal to:

4

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10

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12

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Solution

The correct option is C $10$
Case $1$ : When $\sqrt{x} \geq 2$
$\sqrt{x} - 2 + x - 4 \sqrt{x} + 2 = 0 \Rightarrow x - 3 \sqrt{x} = 0 \Rightarrow x = 0, x = 9$
As, $\sqrt{x} \geq 2 \Rightarrow x = 9$

Case $2$ : When $\sqrt{x} < 2$
$2 - \sqrt{x} + x - 4 \sqrt{x} + 2 = 0 \Rightarrow x - 5 \sqrt{x} + 4 = 0 \Rightarrow (\sqrt{x} - 4) (\sqrt{x} - 1) = 0 \Rightarrow x = 1, 16$
As, $\sqrt{x} < 2 \Rightarrow x = 1$

Hence, sum $= 9 + 1 = 10$

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The sum of the solutions of the equation |√x−2|+√x(√x−4)+2=0, (x>0) is equal to:

The correct option is C 10Case 1: When √x≥2 √x−2+x−4√x+2=0⇒x−3√x=0⇒x=0,x=9 As, √x≥2⇒x=9 Case 2: When √x<2 2−√x+x−4√x+2=0⇒x−5√x+4=0⇒(√x−4)(√x−1)=0⇒x=1,16 As, √x<2⇒x=1 Hence, sum =9+1=10

The sum of the solutions of the equation $| \sqrt{x} - 2 | + \sqrt{x} (\sqrt{x} - 4) + 2 = 0, (x > 0)$ is equal to: