數學兩題(唔識)

題目1:

If x+y=4 and xy=15/4 , find x^2+y^2.

x^2+y^2
=x^2+(2xy)+b^2-(2xy) <------利用 (a+b)^2 = a^2+2ab+b^2
=(x+y)^2 - 2xy
=(4)^2 - 2(15/4)
=17/2


題目2:

某數列的通項是8n+1, 下列哪個那個數是該數列的第n+1項與第n項的差?

T(n) = 8n+1　＜－－－－第n項

T(n+1) = 8(n+1)+1 = 8n+9　＜－－－－第n+1項

T(n+1) T(n)
=(8n+9) - (8n+1)
=8

所以，答案是Ｃ

2009-09-08 19:47:54 補充：
PS:打錯野

以下是正確的

T(n+1)-T(n)
=(8n+9) - (8n+1)
=8

1. Consider (x + y)2 = (x2 + y2) + 2xy

x2 + y2 = (x + y)2 - 2xy

= (4)2 - 2(15/4)

= 17/2


2. 第n + 1項與第n項的差

= [8(n + 1) + 1] - (8n + 1)

= (8n + 9) - (8n + 1)

= 8

答案是c