中二數學....急

1. 4x+3=3x+4
(左方x的係數不等於右方的係數) -->左方不等於右方,不是恆等式

2. 5(2x-3)=2(5x-1)-13
左方 = 10x-15
右方 = 10x-2-13 = 10x-15 =左方
是恆等式

3. (x-3)^2=(3-x)^2
左方 = (x-3)(x-3) = x^2 - 6x+9
右方 = (3-x)(3-x) = 9-6x+x^2 = x^2-6x+9 =左方
是恆等式

4. (2x-3)(x+4)=(2x+3)(x-4)
左方 = (2x-3)(x+4) = 2x(x+4)-3(x+4) = 2x^2 +8x-3x-12 = 2x^2+5x-12
右方 = (2x+3)(x-4) = 2x(x-4)+3(x-4) = 2x^2-8x+3x-12 = 2x^2-5x-12不等於左方
不是恆等式

5. (x+A)(x-2)≣Bx^2+x-6
左方 = x(x-2)+A(x-2) = x^2 + (A-2)x -2A
右方 = Bx^2 +x-6
B = 1, A-2 = 1, A=3

6. (A+B)x+B≣5x-3
A+B = 5 及 B = -3
A = 5-(-3) = 8

7. (Ax-2)^2≣9x^2+12x+B
左方 = Ax(Ax-2) - 2(Ax-2) = A^2x^2 -4Ax + 4
A^2 = 9 及 -4A = 12 及 B = 4
A = -3及 B = 4

8. (x+A)(x+2)≣x^2+Bx-6
左方 = x(x+2)+A(x+2) = x^2 + (2+A)x+2A
2+A = B 及 2A = -6
A = -3
B = 2-3 = -1

恆等式
1.
4x+3=3x+4
左方不等於右方,所以不是恆等式

2.
5(2x-3)=2(5x-1)-13
左方： 5(2x-3)=１０x-15
右方：2(5x-1)-13=10x-2-13
=10x-15
左方=右方,所以是恆等式

3. (x-3)²=(3-x)²
左方:(x-3)² = (x-3)(x-3) = x² - 6x+9
右方:(3-x)² = (3-x)(3-x) = 9-6x+x² = x²-6x+9
左方=右方,所以是恆等式


4. (2x-3)(x+4)=(2x+3)(x-4)
左方 = (2x-3)(x+4) = 2x(x+4)-3(x+4) = 2x² +8x-3x-12 = 2x²+5x-12
右方 = (2x+3)(x-4) = 2x(x-4)+3(x-4) = 2x²-8x+3x-12 = 2x²-5x-12
左方不等於右方,所以不是恆等式




求下列各恆等式中常數A和B的值
5. (x+A)(x-2)≣Bx²+x-6
x²-2x+Ax-2A≣Bx²+x-6
x²+A(x-2)-2A≣Bx²+x-6
所以A-2 = 1,B = 1, ,A=3

6. (A+B)x+B≣5x-3

B=-3
(A+B)x=5x
A+B=5
A+-3=5
A=5+3
A=8

7. (Ax-2)²≣9x²+12x+B
(Ax)²-2(Ax)(2)+2²≣9x²+12x+B
A²x²-4(Ax)+4≣3²x²+12x+B
A²x²-Ax+4≣3²x²+3x+B
所以,A=3,b=4

8. (x+A)(x+2)≣x²+Bx-6
x²+2x+Ax+2A≣x²+Bx-6
x²+x(2+A)+2A≣x²+Bx-6
所以,A=-3,
B=2+A=2+3=5

1/ 4x+3=3x+4
L.H.S= 4x+3
R.H.S=3x+4
非恆等式

2/ 5(2x-3)=2(5x-1)-13
L.H.S= 5(2x-3)
=10x -15
R.H.S=2(5x-1)-13
=10x -2 -13
=10x -15
恆等式

3/ (x-3)^2=(3-x)^2
L.H.S= (x-3)^2
R.H.S=(3-x)^2
=[ ( -1)(x -3) ]^2
=(x-3)^2
恆等式

4/ (2x-3)(x+4)=(2x+3)(x-4)
L.H.S=(2x-3)(x+4)
=(-1)(x+4)( -2x+3)
R.H.S=(2x+3)(x-4)
非恆等式

5/ (x+A)(x-2)≣Bx^2+x -6
(x+A)(x-2)=x^2+(A -2)x -2A

-6= -2A
A= 3
B=1

6/ (A+B)x+B≣5x-3
(A+B)x+B=Bx+A+B
B=5
A+B= -3
A+5= -3
A= -8

7/ (Ax-2)^2≣9x^2+12x+B
(Ax-2)^2=A^2x^2 -4Ax +4
A^2=9
A= -3
because 12= -4A
B=4

8/ (x+A)(x+2)≣x^2+Bx -6
(x+A)(x+2)=x^2+(A+2)x+2A
2A= -6
A= -3
B=A+2
B=2 -3
B= -1

恆等式

1. 4x+3=3x+4
不是恆等式

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2. 5(2x-3) = 2(5x-1)-13
左邊 = 5(2x-3) = 10x - 15
右邊 = 2(5x-1)-13 = 10x - 2 - 13 = 10x - 15
左邊 = 右邊 , 所以 5(2x-3) = 2(5x-1)-13 係恆等式
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3. (x-3)^2=(3-x)^2
左邊 = (x-3)^2 = [ -(-x+3) ]^2 = (-x+3)^2 = 右邊 ,
所以 (x-3)^2=(3-x)^2 係恆等式
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4. (2x-3)(x+4) = (2x+3)(x -4)
當 x = 1,
左邊 = (2(1)-3)(1+4) = (-1)(5) = -5
右邊 = (2(1)+3)(1 -4) = (5)(-3) = -15
左邊不等於右邊, 所以 (2x-3)(x+4) = (2x+3)(x -4) 不是恆等式

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求下列各恆等式中常數A和B的值

5. (x+A)(x-2)≣Bx^2+x-6
當 x = 2, 0 = 4B + 2 - 6, B = 1
當 x = 0, (A)(-2) = -6, A = 3
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6. (A+B)x+B≣5x-3
當 x = 0, B = -3
當 x = -1, -A - B + B = -5 - 3, A = 8
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7. (Ax-2)^2≣9x^2+12x+B
當 x = 0, 4 = B
當 x = 1, (A-2)^2≣9+12+B
(A-2)^2≣9+12+4
(A-2)^2≣25
A-2 = 5 or A-2 = -5
A = 7 (rejected) or A = -3
A = -3, B = 4
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8. (x+A)(x+2)≣x^2+Bx-6
當 x = -2, 0 = 4 -2B - 6, B = -1
當 x = 0, (A)(2) = -6, A = -3

2007-10-04 20:36:46 補充：
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