Question

问这四个一元二次方程怎么解，要过程。2（X-1）²-18=0 X²+4X-1=0 9(X+1)

问这四个一元二次方程怎么解，要过程。2（X-1）²-18=0
X²+4X-1=0
9(X+1)²=2(X-5)²
9X-12X-1=0

Answer 1

2（X-1）²-18=0
(x-1)²=9
x-1=±3
x=1±3
x=4或x=-2

X²+4X-1=0
x²+4x+4=1+4
(x+2)²=5
x+2=±√5
x=-2±√5

9(X+1)²=4(X-5)²
(3x+3)²-(2x-10)²=0
(3x+3+2x-10)(3x+3-2x+10)=0
(5x-7)(x+13)=0
x=7/5或x=-13

9X²-12X-1=0
x²-4/3x=1/9
x²-4/3x+(2/3)²=1/9+4/9
(x-2/3)²=5/9
x-2/3=±√5/3
x=2/3±√5/3
所以x=2/3+√5/3或x=2/3-√5/3