Question

2X平方加4X减1等于0的解算答案

Answer 1

解方程:2X²+4X-1=0.
◆解法1(配方法):

2X²+4X-1=0.
X²+2X-1/2=0.
X²+2X+1=3/2.
(X+1)²=3/2.
X+1=±√6/2.
则:X1=-1+√6/2=(-2+√6)/2, X2=-1-√6/2=-(2+√6)/2.
◆解法2(公式法):
2X²+4X-1=0.
则a=2,b=4,c=-1, b²-4ac=16-4*2*(-1)=24.
∴X=[-b±√(b²-4ac)]/(2a)=(-4±√24)/4=(-4±2√6)/4=(-2±√6)/2.

即X1=(-2+√6)/2, X2=(-2-√6)/2=-(2+√6)/2.

Answer 2

2x^2+4x-1=0
x^2+2x=1/2
(x+1)^2=1/2
x+1=土1/2
x1=-1/2 x2=-3/2

Answer 3

2(x^2+2x)=1
x^2+2x=1/2

x^2+2x+1=1/2+1=3/2

(x+1)^2=3/2
x+1=±√6/2
x=-1±√6/2