Question

6x方+6/x方+5x+5/x=38

Answer 1

设x+1/x=t,则有x^2+1/x^2+2=t^2,即有x^2+1/x^2=t^2-2

原方程可以化为:6(t^2-2)+5t=38

6t^2+5t-50=0

(3t+10)(2t-5)=0

t1=-10/3

t2=5/2

故有x+1/x=-10/3

即有x^2+10/3x+1=0

(x+3)(x+1/3)=0

x1=-3,x2=-1/3

x+1/x=5/2

x^2-5/2x+1=0

(x-2)(x-1/2)=0

x3=2,x4=1/2