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The complete solution set of the equation $|x^{2} - 5 x + 6| + |x^{2} + 12 x + 27| = | 17 x + 21 |$ is

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x∈[−9,3]

x∈[−3,2)∪(2,3]

x∈[−9,−3]∪[2,3]

x∈(−2,3)

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detailed solution

Correct option is C

We have x2−5x+6+x2+12x+27=|17x+21|or x2−5x+6+x2+12x+27=x2+12x+27−x2−5x+6⇒ x2−5x+6x2+12x+27≤0⇒ (x−2)(x−3)(x+3)(x+9)≤0From the sign scheme, x∈[−9,−3]∪[2,3]

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The complete solution set of the equation x2−5x+6+x2+12x+27=|17x+21| is

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The complete solution set of the equation $|x^{2} - 5 x + 6| + |x^{2} + 12 x + 27| = | 17 x + 21 |$ is