F.4 maths

2010-10-15 4:23 am
若α和β是二次方程2²-6x+3=0的根,且α>β,求下列各數式的值。(如有需要,答案以根式表示。)

a) α-β

b) α^4-β^4
更新1:

2x²-6x+3=0

更新2:

唔好意思 打漏左個x

更新3:

thx!

回答 (1)

2010-10-15 4:29 am
✔ 最佳答案
是否打錯題目 --- 2^2 ??

2010-10-14 20:29:03 補充:
I change α and β into a and b for me to type conveniently
a + b = -(-6/2) = 3
ab = 3/2
a) a - b
= √(a-b)^2
= √(a^2 - 2ab + b^2)
= √[(a+b)^2 - 4ab]
= √[3^2 - 4(3/2)]
= √(9 - 6)
= √3

b) a^4 - b^4
= (a^2 + b^2)(a^2 - b^2)
= [(a+b)^2 - 2ab](a+b)(a-b)
= [3^2 - 2(3/2)](3)(√3)
= (6)(3√3)
= 18√3
參考: Knowledge is power.


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