(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


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