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The AM between two positive numbers a and b(a > b) is twice th

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The AM between two positive numbers a and $b (a > b)$ is twice their GM. Prove that $a : b = (2 + 3) : (2 - 3)$ .

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The AM between two positive numbers a and

b (a > b)

is twice their GM. Prove that

a : b = (2 + 3) : (2 - 3)

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Given,

A M = 2 (GM)

\Rightarrow \frac{1}{2} (a + b) = 2 ab \Rightarrow \frac{a + b}{2 ab} = \frac{2}{1}

\Rightarrow \frac{a + b + 2 ab}{a + b - 2 ab} = \frac{2 + 1}{2 - 1}

\Rightarrow \frac{( a + b ) ^{2}}{( a - b ) ^{2}} = \frac{( 3 ) ^{2}}{( 1 ) ^{2}}

\Rightarrow \frac{a + b}{a - b} = \frac{3}{1}

\Rightarrow \frac{( a + b ) + ( a - b )}{( a + b ) - ( a - b )} = \frac{3 + 1}{3 - 1}

\Rightarrow \frac{a}{b} = \frac{3 + 1}{3 - 1}

\Rightarrow \frac{a}{b} = \frac{( 3 + 1 ) ^{2}}{( 3 - 1 ) ^{2}} = \frac{2 + 3}{2 - 3}

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Question Text	The AM between two positive numbers a and $b (a > b)$ is twice their GM. Prove that $a : b = (2 + 3) : (2 - 3)$ .
Answer Type	Text solution:1
Upvotes	150