解方程x^2/3+48/x^2=10(x/3-4/x)
问题描述：
解方程x^2/3+48/x^2=10(x/3-4/x)
答
x^2/3+48/x^2=10(x/3-4/x)
(x^4 + 144)/(3x^3)= 10 (x^2- 12)/ (3x)
x^4 + 144= 10x^2(x^2-12)
9x^4-120x^2+144 =0
x^2 = (120 +96) / 18 or (120 -96) / 18
= 12 or 4/3
x = 2√3 or -2√3 or 2√3/3 or -2√3/3
答
令a=x/3-4/xa²=x²/9-8/3+16/x²所以x²/3+48/x²=3(a²+8/3)=10a3a²-10a+8=0(a-2)(3a-4)=0x/3-4/x=2x²-6x+12=0无解x/3-4/x=4/3x²-4x-4=0x=2-2√2,x=2+2√2