The correct option is B 8
Assuming
y=(x−1)+(x−5)2⇒x−3=y⇒x=y+3
Given equation is
(x−1)4+(x−5)4=82
(y+2)4+(y−2)4=82
⇒(y2+4+4y)2+(y2+4−4y)2=82
⇒2[(y2+4)2+(4y)2]=82⇒(y2+4)2+(4y)2=41⇒y4+24y2−25=0⇒(y2+25)(y2−1)=0
⇒y2−1=0 (y2+25≠0)⇒y=±1⇒x−3=±1⇒x=4,2
Hence, the product of the real roots is 8.