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Consdier the equaiton 2 + |x^(2) + 4x + ...

Consdier the equaiton `2 + |x^(2) + 4x + 3|= m , m in R` Set of all values of m so that the given equaition have two solutions is

A

`(3, oo)`

B

`(2,oo)`

C

`{2} uu (3,oo)`

D

None of these

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The correct Answer is:
To solve the equation \( 2 + |x^2 + 4x + 3| = m \) and find the set of all values of \( m \) such that the equation has two solutions, we can follow these steps: ### Step 1: Rewrite the equation We start by rewriting the equation: \[ |x^2 + 4x + 3| = m - 2 \] This implies that \( m \) must be greater than or equal to 2 because the absolute value is always non-negative.
To solve the equation \( 2 + |x^2 + 4x + 3| = m \) and find the set of all values of \( m \) such that the equation has two solutions, we can follow these steps: ### Step 1: Rewrite the equation We start by rewriting the equation: \[ |x^2 + 4x + 3| = m - 2 \] This implies that \( m \) must be greater than or equal to 2 because the absolute value is always non-negative.
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