If α,β are the roots of x2 – 2ax + b2 = 0 and γ,δ, are the roots of x2 – 2bx + a2 = 0

α + β = 2 a , αβ = b 2 γ + δ = 2 b , γδ = a 2 AM of α , β = GM of γ , δ ( α + β ) 2 = γ δ GMof α , β = AM of γ , δ α β = ( γ + δ ) 2

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If $α, β$ are the roots of x² – 2ax + b² = 0 and $γ, δ$ , are the roots of x² – 2bx + a² = 0

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$α, β, γ, δ$ are in GP

$α, β, γ, δ$ are in AP

Geometric Mean of $α, β$ = Arithmetic Mean of $γ, δ$

Arithmetic Mean of $α, β$ = Geometric Mean of $γ, δ$

answer is A, B.

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Detailed Solution

$\begin{array}{l} α + β = 2 a, αβ = b^{2} \\ γ + δ = 2 b, γδ = a^{2} \\ AM of α, β = GM of γ, δ \\ \frac{(α + β)}{2} = \sqrt{γ δ} \\ GMof α, β = AM of γ, δ \\ \sqrt{α β} = \frac{(γ + δ)}{2} \end{array}$

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