Solution set of the equation (x−1)4+(x−5)4=  82  is

Given equation is (x−1)4+(x−5)4=82 Now splitting −1  as −3+2 , −5  as −2−3 ⇒    (x−3+2)4+(x−3−2)4=82 Let x−3=y ⇒    (y+2)4+(y−2)4=82 ⇒    [(y+2)2(y+2)2]+[(y−2)2(y−2)2]=82 Expand and simplify we get,⇒    2y4+48y2+32=82 ⇒    2(y4+24y2+16)=82 ⇒    y4+24y2−25=0 ⇒    y2=−25,1 ⇒    y=±5i,  ±1 ⇒    x−3  =  ±5i,  ±1    (∵x=y−3) ⇒x=± 5i+3, x=±1+3 ∴  The solution set of given equation is {2,4,3±5i}.