令y = x+2
则(x+1）^4+(x+3)^4
=(y-1)^4 + (y+1)^4
=[(y-1)²+(y+1)²]² - 2(y-1)²(y+1)²
=(2y²+2)² -2(y²-1)²
=4y^4 + 8y² + 4 - 2y^4 +4y²-2
=2y^4 + 12y²+2 = 82
所以
y^4 + 6y² = 40
(y²+3)² = 49
y²+3 = 7
y² = 4
y=±2
x=0,或x=-4