The roots of the equation (3−x)4+(2−x)4=(5−2x)4  are

The given equation is (3−x)4+(2−x)4=(5−2x)4         ……(i) Put 3−x=a  and 2−x=b Eq. (i) be comes a4+b4=(a+b)4 ⇒a4+b4=a4+b4+4a3b+6a2b2+4ab3 ⇒ 2ab(2a2+3ab+2b2)=0          ∴   a=0⇒3−x=0⇒x=3       b=0⇒2−x=0 ⇒ x=2 and  2a2+3ab+2b2=0         2(ab)2+3(ab)+2=0        ab=−3±9−164       3−x2−x=−3±i74 ⇒  3−x2−x−1=−7±i74 ⇒  12−x=−7±i74     2−x=4−7±i7     x−2=4−7±i7         x=−18±2i7−7±i7 Taking ‘+’ sign       x=(−18+2i7)(−7−i7)(−7+i7)(−7−i7)           =140+4i756 ∴   x=35+i714 Taking ‘-‘ sign,    x=35−i714 Hence, roots of Eq. (i) are 2,3,35±i714 i.e.,   Two real and two imaginary.