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Question

The product of the real roots of the equation (x1)4+(x5)4=82 is

A
25
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B
8
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C
8
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D
25
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Solution

The correct option is B 8
Assuming
y=(x1)+(x5)2x3=yx=y+3

Given equation is
(x1)4+(x5)4=82
(y+2)4+(y2)4=82
(y2+4+4y)2+(y2+44y)2=82
2[(y2+4)2+(4y)2]=82(y2+4)2+(4y)2=41y4+24y225=0(y2+25)(y21)=0
y21=0 (y2+250)y=±1x3=±1x=4,2

Hence, the product of the real roots is 8.

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