F.4 Maths

If the answer is 21, then the roots should be α+1 and β+1.
Could you also tell us the result of (αβ)^2? Is it 4?

2013-12-30 22:56:43 補充：
According to your answer given, the roots should be α+1 and β+1.

2013-12-31 23:58:17 補充：
新年進步！萬事勝意！身體健康！心想事成！

2013-12-31 23:59:57 補充：
新年進步！

萬事勝意！

身體健康！

心想事成！

2014-01-01 00:08:58 補充：
Happy New Year!

新年進步！

萬事勝意！

身體健康！

心想事成！

2014-01-01 11:50:42 補充：
版主唔confirm, 咁點答？

2014-01-01 15:49:05 補充：
若 α^2 + β^2 = 21，那應該是印刷錯誤。原題目應該是：Given that α+1 and β+1 are the roots of the quadratic equationx^2 + 3x - 2 = 0(a) Find the values of (αβ)^2 and (α^2 + β^2)
Sum of roots = (α + 1) + (β + 1) = -3So, α + β = -5 ...........(1)Product of roots (α + 1)(β + 1) = -2αβ + (α + β) + 1 = -2αβ - 5 + 1 = -2 ......... (from (1))αβ = 2 ...................... (2)Therefore, (αβ)^2 = 4
Also, (α + β)^2 = α^2 + 2αβ + β^2From (1), (2), we get(-5)^2 = α^2 + β^2 + 2(2)Therefore, α^2 + β^2 = 21
(As you state that this is part (a), so I think the part (b) question is :Form a quadratic equation with roots α^2 and β^2.And the solution is :x^2 - 21x + 4 = 0)

唔怪之得我計來計去都計唔到啦！覺得自己好鬼蠢呀！

α+1 and β-1 ???

2013-12-31 20:34:46 補充：
阿年，你答左佢啦～

祝大家新年進步～

開開心心、健健康康～

2014-01-01 08:53:16 補充：
好好好~

大家咁話~

(◕‿◕✿)

2014-01-01 14:18:15 補充：
版主是一個好乖的學生～

我之前跟她溝通過幾次～

相信是打題有誤～

而且在程度上看，該題目如果是α+1 and β-1 則太難了～
也不能用 sum and product of roots~

所以你作答時只要註明回答的是假設了α+1 and β+1，那就是最佳解答。

正如昨晚那題排容奧數我都是這樣答，否則沒人能答。

本題你已作了豐富且適當的分析。

α - β = +/-sqrt (α - β)^2
α^2 +β^2 = (α + β)^2 -2αβ