If-a-b-ab-4-1-then-a-b-a-gt-b-

Question Number 177648 by BaliramKumar last updated on 07/Oct/22

I f \frac{a + b}{\sqrt{a b}} = \frac{4}{1} t h e n a : b = ? [a > b]

Answered by Rasheed.Sindhi last updated on 07/Oct/22

a + b = 4 \sqrt{a b}

a^{2} + b^{2} = 16 a b - 2 a b = 14 a b

\frac{a}{b} + \frac{b}{a} = 14

x + \frac{1}{x} = 14; [\frac{a}{b} = x]

x^{2} - 14 x + 1 = 0

x = \frac{14 \pm \sqrt{196 - 4}}{2} = \frac{14 \pm 8 \sqrt{3}}{2} = 7 \pm 4 \sqrt{3}

\frac{a}{b} = \frac{7 \pm 4 \sqrt{3}}{1}

∵ a > b

∴ a : b = (7 + 4 \sqrt{3}) : 1

Commented by BaliramKumar last updated on 07/Oct/22

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