解方程 1.4X^2-256=0 2. 4(x-2/1)^2=1 3. -x^2+2x+3=0 4. 3x^2+8x-3=0 答案是X1和X2=多少,要有過程

1.4X^2-256=0
4x^2=256
x^2=64
x1=8,x2=-8
2. 4(x-1/2)^2=1
(x-1/2)^2=1/4
x-1/2=1/2, x-1/2=-1/2
x1=1/2+1/2=1
x2=-1/2+1/2=0
3. -x^2+2x+3=0
x^2-2x-3=0
(x-3)*(x+1)=0
x1=3, x2=-1
4. 3x^2+8x-3=0
(3x-1)*(x+3)=0
x1=1/3
x2=-3

不解方程,求下列方程兩根x1,x2的和與積(1)x^2-2x-1=0.(2)2x^2-3x-1=0.(3)3x^2-4=0.

(1)x^2-2x-1=0.
x1+x2=2
x1x2=-1
(2)2x^2-3x-1=0.
x1+x2=3/2
x1x2=-1/2
(3)3x^2-4=0.
x1+x2=4/3
x1x2=0
(4)4x^2+2x-3=0.
x1+x2=-1/2
x1x2=-3/4

懈方程:(1)x2-4x+3=0(2)x2+2x-1=0

(1)分解因式得:(x-1)(x-3)=0,
可得x-1=0或x-3=0,
解得:x1=1,x2=3;

(2)方程變形為x2+2x=1,
配方得:x2+2x+1=2,即(x+1)2=2,
開方得:x+1=±

2


則x1=-1+

2

,x2=-1-

2

不解方程2x∧2+3x-1=0,求x1∧2+x2^2的值

2x²+3x-1=0
x1+x2=-3/3
x1x2=-1/2
x1²+x2²=(x1+x2)²-2x1x2=(-3/2)²-2*(-1/2)=9/4+1=13/4

解方程:1. 20x^2+253x+800=0 2. x^2-3|x|-4=0

1. 20x^2+253x+800=0
(4x+25)(5x+32)=0
x1=-25/4 x2=-32/5
2. x^2-3|x|-4=0
當x<0時
原式=x^2+3x-4=0
(x+4)(x-1)=0
x1=-4 x2=1
x2=1不符合條件 (捨去)
當x>0時
原式=x^2-3x-4=0
(x-4)(x+1)=0
x3=4 x4=-1
x4=-1不符合條件 (捨去)
方程的解為X1=-4 X2=4

已知方程3x²-4x=-1的兩根是x1 x2,不解方程,求: 1.x2/x1 + x1/x2 2.(x1 - 2)(x2 - 2)

解:方程3x²-4x=-1可化為:3x²-4x+1=0
由根與係數的關係,有
x1+x2=4/3, x1x2=1/3
∴x2/x1 + x1/x2
=(x1²+x2²)/(x1x2)
=[(x1+x2)²-2x1x2]/(x1x2)
=[(4/3)²-2×(1/3)]/(1/3)
=[(16/9)-(2/3)]/(1/3)
=(10/9)/(1/3)
=10/3

(x1-2)(x2-2)
=x1x2-2x1-2x2+4
=x1x2-2(x1+x2)+4
=(1/3)-2×(4/3)+4
=(1/3)-(8/3)+4
=(-7/3)+4
=5/3.

用換元法解方程:(x-2)/x減去3x/(x-2)=2.答案是x1=1,x2=-1.一定要過程!

設t=x/(x-2)
原式=(1/t)-3t=2
t1=-1,t2=1/3
代回x1=1,x2=-1
不好意思,打錯了,剛t多打了個3

若方程2X^2-8X-3=0的兩個根是X1,X2,則(X1)^3+(X2)^3=

由韋達定理可知:
X1+X2=-(-8)/2=4 X1X2=-3/2
(X1)^3+(X2)^3
=(X1+X2)(X1^2-X1X2+X2^2)
=(X1+X2)[(X1+X2)^2-2X1X2-X1X2]
=(X1+X2)[(X1+X2)^2-3X1X2]
=4×[4^2-3×(-3/2)]
=82

方程2x2-3x+1=0的兩個根為x1,x2,不解方程,求x1-x2的值

∵方程2x2-3x+1=0的兩個根為x1,x2
∴x1+x2=

3
2

,x1x2=

1
2


∴(x1-x22=(x1+x22-4x1x2=

9
4

-2=

1
4


則x1-x2

1
2

設方程2x2-3x+1=0的兩根x1,x2,不解方程,求|x1-x2|的值

由韋達定理知x1+x2=

3
2

,x1?x2=

1
2


∴|x1-x2|=

(x1+x2)2?4x1x2

=

9
4

?4×

1
2

=

1
2

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