Sum of values of x, satisfying the equation √3x2+6x+7+√5x2+10x+14=4−2x−x2, is
A
−3
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B
−1
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C
0
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D
3
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Solution
The correct option is B−1 We have, √3x2+6x+7+√5x2+10x+14=4−2x−x2 ⇒√3(x+1)2+4+√5(x+1)2+9=5−(x+1)2
The minimum value of √3(x+1)2+4 is 2 at x=−1 and the minimum value of √5(x+1)2+9 is 3 at x=−1. So, the minimum value of LHS is 5 at x=−1. RHS has maximum value 5 at x=−1.