小學代數

[chanchiwai]

題目：4個人的年齡是4個連續數，他的積是120
咁他的和是？
請寫出計法。

[hangchoi]

their ages are x, x+1, x+2 and x+3

So, x (x+1) (x+2) (x+3) = 120, i.e. x^4+6x^3+11x^2+6x = 120

since x is an integer and if x = 4, x^4 = 256 > 120, then x must be < 4.

Putting x = 3, 3(4)(5)(6) = 360 > 120, and you will find out x = 2 and their ages are 2, 3, 4, 5.

Their sum is then 14

[chin]

their ages are x, x+1, x+2 and x+3

So, x (x+1) (x+2) (x+3) = 120, i.e. x^4+6x^3+11x^2+6x = 120

since x is an integer and if x = 4, x^4 = 256 > 120, then x must be < 4.

Putting x = 3, 3(4)(5)(6) = 360 > 120, and you will find out x = 2 and their ages are 2, 3, 4, 5.

Their sum is then 14

Very good!
I missed the 2nd step about X^4=256>120 part.

[chanchiwai]

我細妹話係某小六升中一面試題目

重有另外兩條

[chanchiwai]

題目2：有10位同學在活動中每人向其他9人握手，10個人共互相握手多少次？

[chanchiwai]

問題3: 有四個盒，每個盒子裝不少於兩個波，任何三個盒加起來不少於八個波，這四個盒至少有多少個波？

[hangchoi]

題目2：有10位同學在活動中每人向其他9人握手，10個人共互相握手多少次？

10C9 = 45 ??

[hangchoi]

問題3: 有四個盒，每個盒子裝不少於兩個波，任何三個盒加起來不少於八個波，這四個盒至少有多少個波？

11

[oo8]

問題3: 有四個盒，每個盒子裝不少於兩個波，任何三個盒加起來不少於八個波，這四個盒至少有多少個波？

3 + 3 + 3 + 2 . . . .= 11

[oo8]

題目2：有10位同學在活動中每人向其他9人握手，10個人共互相握手多少次？

小學時的計算方法：

9+8+7+6+5+4+3+2+1 = 45