Question
(α,β);(β,γ) &(γ,α) are respectively the roots of x²-2px+2=0, x²-2qx+3=0,x²-2rx+6=0. if α,β,γ are all positive , then the value of p+q+r is
Joshi sir comment
According to the given conditions
α+β=2p (1) α*β=2 (2)
β+γ=2q (3) β*γ=3 (4)
γ+α=2r (5) γ*α=6 (6)
so α+β+γ = p+q+r (7)
and α*β*γ=6 (8)
dividing eq. (8) by (2), (4) , (6) one by one we will get α, β, γ hence we will get p+q+r