39centroid= [ (α+β+γ)/3, Σ (αβ/3αβγ)]
α+β+γ=3p
Σαβ=3q
αβγ=1
so centroid is [p,q]
If α,β and γ are the real roots of the equation x3 – 3px2 + 3qx – 1 = 0, then the centroid of the triangle with vertices (α,1/α) , (β,1/β) and (γ,1/γ) is:
I guess one of the easier QOD's
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5 Answers
39
3put x=1/x in the given eqn we will get the eqn whose roots are 1/α,1/β,1/γ
so find the sum of roots of the two eqn helps to solve the problem.
62could someone express what bhargav has given in a even simpler way?
62I mean it wont be of much materila difference.. the result will be the same but was just wondering if someone could post of "different" logic for finding 1/a+1/b+1/c