方程x^2+16x^2/(x-4)^2=84求解.
问题描述：
方程x^2+16x^2/(x-4)^2=84求解.
答
x²+16x²/(x-4)² = 84
令 y=x-4,则
(y+4)²+16(y+4)²/y² = 84
(y+4)²(1+16/y²) = 84
(y+4)²(y²+16)/y² = 84
(y²+8y+16)(y²+16)/y² = 84
(y+16/y+8)(y+16/y) = 84
令 z=y+16/y
(z+8)z = 84
z²+8z-84 = 0
(z+14)(z-6) = 0
z=6 或 z=-14
代入得 y + 16/y = 6 (无解) 或 -14 ,得 y = -7 ± √33
∴ x = -3 ± √33