Question

# value of x satisfying the equality $$|x^2 + 8x + 7| = |x^2 + 4x + 4| + |4x + 3|$$ for $$x \in R$$ are

A
(2,)
B
(34,){2}
C
[34,){2}
D
(43,)

Solution

## The correct option is C $$(-2, \infty)$$As we know$$|a|+|b|=|a+b|$$$$ab\ge0$$$$\implies (x^2+4x+4)(4x+3)\ge0$$$$\implies (x+2)^2(4x+3)\ge 0$$$$\implies x\in[-\dfrac{3}{4},\infty)\cup$${$$-2$$}Mathematics

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