Solution of inequality x2 - 2-x- - 15 - 0 is given by

The correct option is C 3 ≤ x ≤ 3 For x ^ 2 +2| x | 15 gt;0 Case 1. x≥ 0 x ^ 2 +2x 15 gt;0⇒ x ( x+5 ) 3( x+5 ) gt;0 ⇒( x 3 ) ...

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Standard XII

Mathematics

How to Find the Inverse of a Function

Solution of i...

Question

Solution of inequality $x^{2} + 2 | x | - 15 \geq 0$ is given by

x \leq \sqrt{3}

x \geq \sqrt{3}

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x \leq - 3

x \geq 3

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- 3 \leq x \leq 3

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none of these

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Solution

The correct option is C $- 3 \leq x \leq 3$
For $x^{2} + 2 | x | - 15 > 0$
Case 1. $x \geq 0$
$x^{2} + 2 x - 15 > 0 \Rightarrow x (x + 5) - 3 (x + 5) > 0 \Rightarrow (x - 3) (x + 5) > 0 \Rightarrow x \in (- \infty, - 5] \cup [3, \infty) ∴ x \in [3, \infty)$
Case 2. $x < 0$
$x^{2} - 2 x - 15 < 0 \Rightarrow x^{2} - 5 x + 3 x - 15 < 0 \Rightarrow x (x + 5) + 3 (x - 15) < 0 \Rightarrow (x + 3) (x - 5) < 0$
$\Rightarrow x \in (- 3, 5)$
$∴ x \in (- 3, 0)$
Hence $x \in (- 3, 3)$

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Solution of inequality x2+2|x|−15≥0 is given by

The correct option is C −3≤x≤3For x2+2|x|−15>0Case 1. x≥0x2+2x−15>0⇒x(x+5)−3(x+5)>0⇒(x−3)(x+5)>0⇒x∈(−∞,−5]∪[3,∞)∴x∈[3,∞)Case 2. x<0x2−2x−15<0⇒x2−5x+3x−15<0⇒x(x+5)+3(x−15)<0⇒(x+3)(x−5)<0⇒x∈(−3,5)∴x∈(−3,0)Hence x∈(−3,3)

Solution of inequality $x^{2} + 2 | x | - 15 \geq 0$ is given by