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Area of Square

If α,β are ...

Question

If $α, β$ are the roots of $x^{2} - 2 a x + b^{2} = 0$ and $γ, δ$ are the roots of $x^{2} - 2 b x + a^{2} = 0$ , then

A

A M

of

α, β = G M

of

γ, δ

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B

G M

of

α, β = A M

of

γ, δ

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C

α, β, γ, δ

a n d i n

AP$

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D

α, β, γ, δ

and in

G P

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Solution

The correct options are
A $G M$ of $α, β = A M$ of $γ, δ$
C $A M$ of $α, β = G M$ of $γ, δ$
$α + β = 2 a, α β = b^{2}$
$γ + δ = 2 b, γ δ = a^{2}$
Clearly we can see from equations that
$\frac{α + β}{2} = \sqrt{γ δ}$
$\sqrt{α β} = \frac{γ + δ}{2}$
Therefore, $G M$ of $α, β = A M$ of $γ, δ$
Hence, options 'A' and 'B' are correct.

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