If a, α are the roots of the equation x^2 + 16x+ 69 =0 and a,β are the roots of the given equation x^2 -2x -35=0 ,without solving the two given equations,find the values of
a) β -α ,
b) α / β
Maths
2007-10-28 11:43 pm
回答 (3)
2007-10-28 11:55 pm
✔ 最佳答案
a+ α = -16 and aα = 69a + β = 2 and aβ = -35
(a) Consider a+ α = -16...(1) and a + β = 2 ...(2)
(2) - (1) a+β - (α+a) = 2 - (-16)
β -α = 18
(b) Consider aα = 69 ...(3) and aβ = -35 ...(4)
(3)/(4) : α / β = 69/(-35) = -69/35
2007-10-29 12:10 am
a+ α = -16 and aα = 69
a + β = 2 and aβ = -35
(a) Consider a+ α = -16...(1) and a + β = 2 ...(2)
(2) - (1) a+β - (α+a) = 2 - (-16)
β -α = 18
(b) Consider aα = 69 ...(3) and aβ = -35 ...(4)
(3)/(4) : α / β = 69/(-35) = -69/35
a + β = 2 and aβ = -35
(a) Consider a+ α = -16...(1) and a + β = 2 ...(2)
(2) - (1) a+β - (α+a) = 2 - (-16)
β -α = 18
(b) Consider aα = 69 ...(3) and aβ = -35 ...(4)
(3)/(4) : α / β = 69/(-35) = -69/35
2007-10-28 11:57 pm
a + α = -16
a x α = 69
a + β = 2
a x β = -35
so,, β -α = (a + β) - (a + α)
= 2 - (-16)
= 18
also,, α / β = (a x β) / (a x α) = -35 / 69
2007-10-28 15:59:09 補充：
錯左@@also,, α / β = (a x β) / (a x α) = -35 / 69應該係(a x α) / (a x β) = -69/35 先岩@@
a x α = 69
a + β = 2
a x β = -35
so,, β -α = (a + β) - (a + α)
= 2 - (-16)
= 18
also,, α / β = (a x β) / (a x α) = -35 / 69
2007-10-28 15:59:09 補充：
錯左@@also,, α / β = (a x β) / (a x α) = -35 / 69應該係(a x α) / (a x β) = -69/35 先岩@@
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