Question

2x-1/x=4x/（2X的平方-1）+3

Answer 1

2x-1/x-4x/(2x^2-1)=3 (2x^2-1)/x-4x/(2x^2-1)-3=0 设(2x^2-1)/x=a a-4/a-3=0 a^2-3a-4=0 (a-4)(a+1)=0 a=4或a=-1 (1)a=4 (2x^2-1)/x=4 2x^2-4x-1=0 x1+x2=2,x1*x2=-1/2 x1^2+x2^2=(x1+x2)^2-2x1x2=5 (2)a=-1 (2x^2-1)/x=-1 2x^2+x-1=0 x3+x4=-1/2,x3*x4=-1/2 x3^2+x4^2=(x3+x4)^2-2x3x4=5/4 x1^2+x2^2+x3^2+x4^2=5+5/4=25/4