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Question

The sum of all real values of x satisfying the equation
(x25x+5)x2+4x60=1 is

A
4
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B
6
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C
5
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D
3
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Solution

The correct option is D 3
(x25x+5)x2+4x60=1

(x25x+5)0

x2+4x60=0

Solving for x.

x=10,6

And, x25x+5

1a=1 or bo=1 or (1)x=1

x25x+5=1

x25x+4=0

(x4)(x1)=0

x=4 or 1

Or

x25x+5=1

x25x+6=0

(x3)(x2)=0

x=3,2

2 will satisfy not 3 because power will be odd

Hence x={10,1,2,4,6}

sum of solutions =3

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