Math, asked by bankimchroy, 9 months ago

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Answered by dhruvinhamel
1

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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