Question

解方程：2x^2=3x+2；0.25X^2+2.5x-6=0;(x+2)^2=6x+7;x^2-2根号3x-6=0 (过程及两种做法）

Answer 1

2x^2=3x+2
2x^2-3x-2=0
(2x+1)(x-2)=0
x=-1/2 或 x=2

2x^2=3x+2
x^2-3/2x-1=0
x^2-3/2x+(3/4)^2-(3/4)^2-1=0
(x-3/4)^2=25/16
x-3/4=5/4或x-3/4=-5/4
x=2或x=-1/2

0.25X^2+2.5x-6=0;
X^2+10x-24=0
(x-2)(x+12)=0
x=2 或x=-12

0.25X^2+2.5x-6=0;
X^2+10x-24=0
X^2+10x+25-25-24=0
(x+5)^2=49
x+5=7或x+5=-7
x=2 或x=-12

(x+2)^2=6x+7;
x^2+4x+4-6x-7=0
x^2-2x-3=0
(x-3)(x+1)=0
x-3=0或x+1=0
x=3 或x=-1
(x+2)^2=6x+7;
(x+2)^2-6(x+2)+5=0
((x+2)-5)((x+2)-1)=0
(x-3)(x+1)=0
x-3=0或x+1=0
x=3 或x=-1

x^2-2根号3x-6=0
x^2-2根号3x+3-3-6=0
(x-根号3)^2=9
x-根号3=3或x-根号3=-3
x=3+根号3 或x=-3+根号3

x^2-2根号3x-6=0
x^2-2根号3x+3-3-6=0
(x-根号3)^2=9
x-根号3=3或x-根号3=-3
x=3+根号3 或x=-3+根号3

x^2-2根号3x-6=0
用公式法解得
x=(2根号3+根号12+4*1*6)/2=3+根号3
或x=(2根号3-根号12+4*1*6)/2=-3+根号3

Answer 2

2x^2=3x+2
2x^2-3x-2=0
(2x+1)(x-2)=0
x=-1/2 或 x=2

2x^2=3x+2
x^2-3/2x-1=0
x^2-3/2x+(3/4)^2-(3/4)^2-1=0
(x-3/4)^2=25/16
x-3/4=5/4或x-3/4=-5/4
x=2或x=-1/2

0.25X^2+2.5x-6=0;
X^2+10x-24=0
(x-2)(x+12)=0
x=2 或x=-12

0.25X^2+2.5x-6=0;
X^2+10x-24=0
X^2+10x+25-25-24=0
(x+5)^2=49
x+5=7或x+5=-7
x=2 或x=-12

(x+2)^2=6x+7;
x^2+4x+4-6x-7=0
x^2-2x-3=0
(x-3)(x+1)=0
x-3=0或x+1=0
x=3 或x=-1
(x+2)^2=6x+7;
(x+2)^2-6(x+2)+5=0
((x+2)-5)((x+2)-1)=0
(x-3)(x+1)=0
x-3=0或x+1=0
x=3 或x=-1

x^2-2根号3x-6=0
x^2-2根号3x+3-3-6=0
(x-根号3)^2=9
x-根号3=3或x-根号3=-3
x=3+根号3 或x=-3+根号3

x^2-2根号3x-6=0
x^2-2根号3x+3-3-6=0
(x-根号3)^2=9
x-根号3=3或x-根号3=-3
x=3+根号3 或x=-3+根号3

x^2-2根号3x-6=0
用公式法解得
x=(2根号3+根号12+4*1*6)/2=3+根号3
或x=(2根号3-根号12+4*1*6)/2=-3+根号3

Answer 3

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