If $a$ is the A.M. of $b$ and $c$ and the two geometric mean are $G_{1}$ and $G_{2},$ then prove that $G_{1}^{3} + G_{2}^{3} = 2 a b \cdot$

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a

is the A.M. of

b

and

c

and the two geometric mean are

G_{1}

and

G_{2},

then prove that

G_{1}^{3} + G_{2}^{3} = 2 a b \cdot

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Question Text

a

is the A.M. of

b

and

c

and the two geometric mean are

G_{1}

and

G_{2},

then prove that

G_{1}^{3} + G_{2}^{3} = 2 a b \cdot

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