Question

高一数学题(圈起来的那三题)

Answer 1

14. √3*x²-x²-4x+3+√3=0
(√3*x²-4x+√3)-(x²-3)=0
(√3*x-1)(x-√3)-(x+√3)(x-√3)=0
(x-√3)(√3*x-1-x-√3)=0
(x-√3)(√3*x-x-1-√3)=0
x1=√3； x2=(1+√3)/(√3-1)=(4+2√3)/2=2+√3
16. 4x⁴ -13x²+1=0
4x⁴ -4x²+1-9x²=0
(2x²-1)²-(3x)²=0
(2x²+3x-1)(2x²-3x-1)=0
2x+3x-1=0， x1、2=[-3±√17]/4
2x²-3x-1=0, x3、4=[3±√17]/4
17. (x-1)(x-3)(x+2)(x+4)+24=0
[(x-1)(x+2)][(x-3)(x+4)]+24=0
(x²+x-2)(x²+x-12)+24=0
(x²+x-2)[(x²+x-2)-10]+24=0
(x²+x-2)²-10(x²+x-2)+24=0
(x²+x-2-4)(x²+x-2-6)=0
(x²+x-6)(x²+x-8)=0
(x+3)(x-2)(x²+x-8)=0
x1=-3
x2=2
x3=(-1+√65)/2
x4=(-1- √65)/2