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Answer» We are given that α / β = γ / δ (3) Reciprocating both the sides, we'll get β / α = δ / γ (4) Adding (3) and (4), we'll get => (α / β) + (β / α) = (γ / δ) + (δ / γ) => (α^2 + β^2) /αβ = (γ^2 + δ^2) /γδ Adding 2 on both the sides, => [(α^2 + β^2) /αβ] + 2 = [(γ^2 + δ^2) /γδ] + 2 => (α^2 + β^2 + 2αβ) /αβ = (γ^2 + δ^2 + 2γδ) /γδ => (α + β)^2 /αβ = (γ + δ)^2 /γδ Now, USING α + β = -p, αβ = Q, γ + δ = -r, γδ = m, => (-p)^2 /q = (-r)^2 /m => m.p^2 = q.r^2 Hence proved |
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