f.2 mats 20點

👨🏻‍🏫 學術台數學

[匿名]

2009-12-25 9:59 pm

find the values of A and B in the following identity.

(x-1)^2+(x-A)(x+2)=2x^2-3x+B

更新1:

to cowboy: 我係要搵個value 唔係你所指個d 可能我講得唔係咁清楚啦 example: Ax^2+Bx^3=6x^2+9x^3 THEN,A=6 B=9 唔好意思,之前打得唔太清楚,誤導左你tim- -''sorry about that!!

更新2:

to tonyleung052: SORRY ABOUT THAT! 你既答案係岩但係唔可以代x=-2,when個題目冇提供x=-2 maybe 我比多個example, 2(x+5)+3(x-1)=Ax+B 2x+10+3x-3=Ax+B 5x+7=Ax+B 所以A=5 B=7

回答 (3)

用戶2053

2009-12-25 10:13 pm

✔ 最佳答案

(x-1)^2+(x-A)(x+2)=2x^2-3x+B

when x = - 2 :

(-3)^2 = 2(-2)^2 - 3(-2) + B

9 = 8 + 6 + B

B = - 5

when x = 0 :

(0-1)^2 + (0 - A)(0+2) = B = - 5

1 - 2A = - 5

2A = 6

A = 3

2009-12-25 14:39:40 補充：
可以代x=-2的,題目是等式,x可=任何數,包括 - 2.

或用你的方法 :

(x-1)^2+(x-A)(x+2)=2x^2-3x+B
x^2 - 2x + 1 + x^2 - Ax + 2x - 2A = 2x^2 - 3x + B

2x^2 - Ax + 1 - 2A = 2x^2 - 3x + B

比較x項 :

-Ax = -3x

A = 3

比較常數 :

1 - 2A = B

1 - 2*3 = B

B = - 5

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BaKa`kIn

2009-12-25 11:22 pm

(x-1)^2+(x-A)(x+2)=2x^2-3x+B
x^2-2x+1+x^2+(2-A)x-2A=2x^2-3x+B
2x^2-Ax+(1-2A)=2x^2-3x+B

比較同類項可得:
a= 3
1-2A=b
1-6=b
b=-5

Proof
L.H.S = (x-1)^2+(x-A)(x+2)
= (x-1)^2+(x-3)(x+2)
= 2x^2-3x-5
R.H.S = 2x^2-3x+B
= 2x^2-3x-5
L.H.S = R.H.S

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cowboy

2009-12-25 10:10 pm

x^2-2x+1+x^2-Ax+2x-A=2x^2-3x+B
x^2+x^2-2x^2+3x-2x-Ax+2x=B-1+A
x-Ax=B+A-1
(1-A)x=B-(1-A)
B=(1-A)x+(1-A)
B=(x+1)(1-A)

x-Ax=B+A-1
x-Ax-A=B-1
A(x+1)=x-B+1
A=[(x+1)-B]/(x+1)
A=1-B/(x+1)

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