中二數學的問題!!!~有10點!!吾該~

2009-02-04 12:19 am
1) Which of the following in an identity?
A) x2次 - 4 = ( x - 2)2次
B) 1- 5( x - 1) =6 - 5( x + 2)
C) x( x - 2) + 1= ( x - 1)2次
D) 3x2次 + 8x + 1 = 3x( x - 3) + 2



2)Which of the following is/are identities?
I. (1 + a ) = 1 + 2a + a2次
II. p2次 + q2次 = ( p + q )2次
III. -3x + 12 = 3( x - 4)

A) I only
B) II only
C) I and II only
D) I,II and III



3)If ( x - 2)( x - 1) - x(x - 1) = Px + Q is an identity , find the values of P and Q.



4) Find the unknown constants A and B in 4x2次 + 11x - 3 = ( Ax - 1)( x + B)



5) Expand ( -5y - 8)( -5y - 8).



6) (p + q3次)(q3次 - p)=?



7) If ( 3X + 1)2次 - ( 4x - 3)2次 = Ax2次 + Bx - 8, Find the values of A and B.



8) If ( x - A)2次 + 1 = x2次 + Bx + c , express B and C in terms of A.



9) If ( x + y)2次 = 64 and ( x - y )2次 = 4, xy=?

回答 (2)

2009-02-04 1:05 am
✔ 最佳答案
Q1)
x( x - 2) + 1 = ( x - 1)2次
x2次 - 2x + 1 = ( x-1)2次
answer: C

Q2)
我覺得問題有少少錯。 如果問題係:
Which of the following is/are identities?
I. (1 + a )2次 = 1 + 2a + a2次
II. p2次 + q2次 = ( p + q )2次
III. -3x + 12 = 3( x - 4)
answer: A) I only

Q3)
(x - 2)(x - 1) - x(x - 1) = Px + Q
x^2 - 3x + 2 - x^2 + x = Px + Q
-2x + 2 = Px + Q
By equating the coefficients:
P = -2
Q = 2

Q4)
4x^2 + 11x - 3 = ( Ax - 1)( x + B)
4x^2 + 11x - 3 = Ax^2 + ABx - x - B
4x^2 + 11x - 3 = Ax^2 + (AB-1)x - B
By equating the coefficients:
A = 4
B = 3

Q5)
( -5y - 8)( -5y - 8).
= ( -5y-8 )^2
= 25y^ + 2(-5y)(-8) + 64
= 25y^ + 80y + 64

Q6)
(p + q^3)(q^3 - p)
= (q^3 + p)(q^3 - p)
= (q^3)^2 - p^2
= q^6 - p^2

Q7)
( 3x + 1)^2 - ( 4x - 3)^2 = Ax^2 + Bx - 8
9x^2 + 6x + 1 - ( 16^2 - 24x + 9 ) = Ax^2 + Bx - 8
-7x^2 + 30x - 8 = Ax^2 + Bx - 8
-7x^2 + 30x = Ax^2 + Bx
By equating the coefficients:
A = -7
B = 30

Q8)
( x - A)^2 + 1 = x^2 + Bx + C
x^2 - 2xA + A^2 + 1 = x^2 + Bx + C
x^2 - 2xA + ( A^2 + 1 ) = x^2 + Bx + C
By equating the coefficients:
B = -2A
C = A^2 +1

Q9)
( x + y )^2 = 64
x^2 + 2xy + y^2 = 64..........(1)
( x - y )^2 = 4
x^2 - 2xy + y^2 = 4.............(2)
eq(1) - eq(2):
4xy = 60
xy = 15
參考: myself.. 嚴禁抄襲!!
2009-02-04 12:49 am
1.A
2.B
3.?
Sorry, no time to do the others
參考: me(A)(Olympic Maths Genius)(I got a Gold Medal On that)


收錄日期: 2021-04-23 23:15:48
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090203000051KK01461

檢視 Wayback Machine 備份