IQ題(數學)

Let the age of the youngest sister be x.
Then the age of the second sister is x+1.
And the age of the elder sister is x+2.

x(x+1)(x+2) = 720
x^3 + 3x^2 + 2x - 720 = 0
(x-8) (x^2+11x+90) = 0
x-8 = 0 or x^2+11x+90 = 0 (NO real solutions)
x = 8
Therefore the age of the elder sister is 8+2 = 10.

2013-05-24 22:14:24 補充：
This is not a IQ question.
This is actually a F.4 Maths question involving solving cubic equation in the chapter of polynomials.

2013-05-24 22:18:01 補充：
If you haven't learned about it, it is hard for you to know how x(x+1)(x+2) - 720 = 0 is changed to (x-8) (x^2+11x+90) = 0. Actually, I use the factor theorem which is introduced in "polynomials" that when you put x=8, x(x+1)(x+2) - 720 = 0, therefore (x-8) is a factor of the polynomial.

我地可以用方程(你應該識方程)~

設姐姐是y,則三個姊妺的年齡是一個連續的數是(yx(y+1)x(y+2)/3)
(要加1係因為例如11,12,13,佢地係一個連續數而且係一個加1的關係)


yx(y+1)x(y+2)/3=720
yx(y+1)x(y+2)/3x3=720x3
yx(y+1)x(y+2)=2160
死唔識計...


真實答案係8,9,10(你可能會問我怎樣計出來，我都係問我爹D,佢話自己續個試1..2..3..4..5..6..7..8..9..10。8,9,10!!)

sorry,我係咪好廢~TAT

10歲

因為8*9*10=720

2013-05-24 22:17:37 補充：
原因:

設最小數(8)為y,

y*(y+1)*(y+2)=720