Question

解方程：2(x²+1/x²)-3(x+1/x)-1=0 分解因式：3x²+5xy-2y²+x+9y+4

要具体过程、、尽快、谢谢！

Answer 1

令t=x+1/x,则x²+1/x²=t²-2,原式:2（t²-2)-3t-1=0 即2t²-3t-5=0,解得t=3或者-1/2 即x+1/x=3或x+1/x=-1/2
而x+1/x=5/2,化简得2x²-5x+2=0 即（x-2)(2x-1)=0,解得x=2或1/2
x+1/x=-1化简得x²+x+1=0无解

综上：x=2或1/2

追问

还有分解因式呢？

追答

3X^2+5XY-2Y^2+X+9Y-4
=(x+2y)(3x-y)+x+9y-4
=(x+2y)(3x-y)+(4x+8y-3x+y)-4
=(x+2y)(3x-y)+4(x+2y)-(3x-y)-4
=(x+2y)(3x-y) -(3x-y)+4(x+2y) -4
=(x+2y-1)(3x-y)+4(x+2y-1)
=(x+2y-1)(3x-y+4)