A maths問題 - Ans.fyi 參考答案

A maths問題

2007-11-18 12:13 am

a+b=-3
ab=-1
1.a^3-b^3
--------------------------------------------------------------------------------------------------------------------------------
2. If a and b are the roots of the quadratic equation 2x^2+ax+b=0,where b≠0,find the values of a and b
3. If the equations x^24x+k=0 and 2x^2-3x+k=0 have a common root a,find the values of k

回答 (1)

用戶19809

2007-11-18 12:30 am

✔ 最佳答案

(1)
a³-b³
=(a-b)(a²+ab+b²)
=(a-b)[(a+b)²-ab]
=(a-b)[(-3)²-(-1)]
=10(a-b)
(2)
2x²+ax+b=0
a+b=-a/2---(1)
ab=b/2---(2)
(1)=>3a/2+b=0
b=-3a/2---(3)
Sub (3) into (2)
a(-3a/2)=(-3a/2)/2
-3a²/2=-3a/4
6a²=3a
2a²-a=0
a(a-1)=0
a=0 or a=1
When a=0,
(1)=>b=0
Since b≠0,
a≠0
Therefore a=1---(4)
Sub (4) into (3):
b=-3(1)/2
b=-3/2
Therefore a=1,b=-3/2
(3)
Let the common root be a
a²+24a+k=2a²-3a+k
a²-2a²+24a+3a=0
-a²+27a=0
a(a-27)=0
a=0 or a=27
From the equation x²+4x+k=0
When a=0,k=0;
When a=27,k=-810
Therefore, k=0 or k=-810

👍 0 👎 0