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Question

The sum of real roots of the equation (x1)(x2)(3x1)(3x2)=8x2 is

A
3
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B
4
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C
6
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D
8
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Solution

The correct option is A 3
(x1)(x2)(3x1)(3x2)=8x2(x1)(3x2)(x2)(3x1)=8x2(3x25x+2)(3x27x+2)=8x2(3x+2x5)(3x+2x7)=8
Assuming 3x+2x5=t
t(t2)=8t22t8=0(t4)(t+2)=0t=2,4

When t=2
3x+2x5=23x23x+2=0D=924<0
No real roots.

When t=4
3x+2x5=43x29x+2=0D=8124>0
Real and distinct roots.

Therefore,
The sum of real roots =93=3

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