QJEEM17Ma687a: JEE Main 2017 Mathematics - Class 11 JEEM17Ma687a Solution: If the arithmetic mean of two numbers a and b, a > b > 0, is…

Question

Verified Solution • 2025–26 Session moderate

If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then

\frac{a + b}{a - b}

is equal to :

Accepted Answer

A.T.Q.,

A.M. = 5G.M.

\frac{a + b}{2} = 5 \sqrt{a b}

\frac{a + b}{\sqrt{a b}}

= 10

∴

\frac{a}{b} = \frac{10 + \sqrt{96}}{10 - \sqrt{96}} = \frac{10 + 4 \sqrt{6}}{10 - 4 \sqrt{6}}

Use componendo and Dividendo

\frac{a + b}{a - b} = \frac{20}{8 \sqrt{6}} = \frac{5}{2 \sqrt{6}} = \frac{5 \sqrt{6}}{12}

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