Consider the equation. (x+1)4+(x+3)4=8 The above equation can be written as, (x+2−1)4+(x+2+1)4=8 Let x+2=y (y−1)4+(y+1)4=8 2(y4+6y2+1)=8 y4+6y2−3=0 y2=
−6±√36+12
2
Solve further y2=−3±2√3 Therefore y2=2√3−3 (x+2)2=2√3−3 x2+4x+4=2√3−3 x2+4x+7−2√3=0 Thus, the product of the roots is, P=