The equation (3−x)4+(2−x)4=  (5−2x)4  has

The given equation is (3−x)4+(2−x)4=  (5−2x)4 Let a=(3−x) , b=(2−x)  ⇒a4+b4  =  (a+b)4⇒    a4+b4=  (a2+2ab+b2)(a2+2ab+b2)⇒    a4+b4  =a4  +4a3b+6a2b2+4ab3+b4⇒    4a2b+6a2b2+4ab3=0⇒    2ab  (2a2+3ab+2b2)=0⇒    a=0  (or)  b=0  (or)  2a2+3ab+2b2=0⇒(3−x)4=0 (or) ⇒(2−x)4=0 (or)2(3−x)2+3(3−x)(2−x)+2(2−x)2=0⇒    x=3  (or) x=2 (or)  7x2−35x+44=0Since  7x2−35x+44=0  has non-real roots,therefore, the given equation have only two real roots.