Question

数学问题（配方法）

X²-X-¾=0
4X²-X-9=0
要详细解答

Answer 1

X²-X-¾=0,两边同乘以4
4X^2-4x-3=0，十字相乘
(2X-3)(2X+1)=0
x=3/2,或x=-1/2

4X²-X-9=0，配成平方式
（2X-1/4）^2-9-1/16=0
(2X-1/4）^2=145/16,两边各开根号
2X-1/4=(√145)/4,或-2X+1/4=(√145)/4
x=(1+√145)/4，或x=(1-√145)/4

Answer 2

X²-X-¾=0
X²-X+(1/4)-1=0
(X-1/2)²=1
得 X-1/2=1 X=3/2
或 X-1/2=-1 X=-1/2

4X²-X-9=0
X²-(1/4)X-9/4=0
X²-(1/4)X+1/64-9/4-1/64=0
(X-1/8)²=145/64
得 X-1/8=√145/8 X=(1+√145)/8
或 X-1/8=-√145/8 X=(1-√145)/8

Answer 3

x²-x+1/4=3/4+1/4=1
(x-1/2)²=(±1)²
x-1/2=±1
x=-1/2,x=3/2

x²-x/4=9/4
x²-x/4+1/64=9/4+1/64=145/64
(x-1/8)²=(±√145/8±√145/8)²
x-1/8=±√145/8
x=(1-√145)/8，x=(1+√145)/8

Answer 4

解答就在这个图中