F.4 Maths
2013-10-07 7:51 pm
Suppose α and β are the roots of the equation x2 - 7x - 3 = 0. Form a quadratic equation with roots α/β and β/α.
回答 (2)
2013-10-07 9:21 pm
✔ 最佳答案
α + β = 7 and αβ = -3Let the required equation be x^2 + px + q = 0
So,
p = -(α/β + β/α)
= -(α^2 + β^2)/(αβ)
= -[(α + β)^2 - 2αβ]/(αβ)
= -(7^2 + 6)/(-3)
= 55/3
q = (α/β)(β/α) = 1
Therefore, the required equation is :
x^2 + 55x/3 + 1 = 0
==> 3x^2 + 55x + 3 = 0
2013-10-07 8:13 pm
首先，從原式 x² - 7x - 3 = 0 得到 α+β = 7 ; αβ= -3
假設以 α/β 和 β/α 為根的方程是 X² + hX + k = 0
α/β + β/α = (α² + β²)/αβ = -h
(α/β)(β/α) = 1 ; k = 1
(α² + β²)/αβ = -h
(α² + β²)/(-3) = -h
(α² + β²) = 3h
(α + β)² = α² + 2αβ + β² = 7² ; then (α² + β²) = .......
假設以 α/β 和 β/α 為根的方程是 X² + hX + k = 0
α/β + β/α = (α² + β²)/αβ = -h
(α/β)(β/α) = 1 ; k = 1
(α² + β²)/αβ = -h
(α² + β²)/(-3) = -h
(α² + β²) = 3h
(α + β)² = α² + 2αβ + β² = 7² ; then (α² + β²) = .......
收錄日期: 2021-04-27 20:35:39
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20131007000051KK00058