If ((a + b)/( (√(ab)))) = (4/1) then a : b = ? [ a>b ]


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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 byBaliramKumar last updated on 07/Oct/22

	$n i c e s o l u t i o n$
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