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Question

Sum of values of x, satisfying the equation 3x2+6x+7+5x2+10x+14=42xx2, 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=42xx2
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.

So the given equation is satisfied only at x=1

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