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If a, b, c are in AP; x is the GM between a and b; y is the GM

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If a, b, c are in AP; x is the GM between a and b; y is the GM between b and c; then show that $b^{2}$ is the AM between $x^{2}$ and $y^{2}$ .

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If a, b, c are in AP; x is the GM between a and b; y is the GM between b and c; then show that

b^{2}

is the AM between

x^{2}

and

y^{2}

12 mins ago

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12 mins ago

Text solutionVerified

Given

a, b, c

are in AP.

∴ (a + c) = 2 b,

Also,

x

is the GM between

a

and

b; y

is the GM between

b

and

c

;

x = ab

and

y = b c

\Rightarrow x^{2} + y^{2} = (ab + b c) = b (a + c) = 2 b^{2}

⟹ b^{2}

is the AM between

x^{2}

and

y^{2}

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Question Text	If a, b, c are in AP; x is the GM between a and b; y is the GM between b and c; then show that $b^{2}$ is the AM between $x^{2}$ and $y^{2}$ .
Answer Type	Text solution:1
Upvotes	150