Find the ratio of; x:y if 10x^2 −9xy +2y^2 =0


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Question Number 72499 by Mr Jor last updated on 29/Oct/19

$F i n d t h e r a t i o o f; x : y i f 10 x^{2} - 9 x y$ $+ 2 y^{2} = 0$
	Answered by Tanmay chaudhury last updated on 29/Oct/19

	$10 x^{2} - 9 x y + 2 y^{2} = 0$ $10 x^{2} - 5 x y - 4 x y + 2 y^{2} = 0$ $5 x (2 x - y) - 2 y (2 x - y) = 0$ $(2 x - y) (5 x - 2 y) = 0$ $w h e n 2 x - y = 0 \to 2 x = y$ $\frac{x}{y} = \frac{1}{2} x : y = 1 : 2$ $w h e n 5 x - 2 y = 0 5 x = 2 y$ $\frac{x}{y} = \frac{2}{5} x : y = 2 : 5$
	Answered by $@ty@m123 last updated on 29/Oct/19

	$D i v i d i n g t h r o u g h o u t b y y^{2},$ $10 k^{2} - 9 k + 2 = 0, w h e r e k = \frac{x}{y}$ $\Rightarrow k = \frac{9 \pm \sqrt{81 - 80}}{20}$ $\Rightarrow k = \frac{9 \pm 1}{20}$ $\Rightarrow k = \frac{1}{2}, \frac{2}{5}$
	Answered by MJS last updated on 29/Oct/19

	$10 x^{2} - 9 x y + 2 y^{2} = 0$ $\frac{x}{y} = \frac{r}{1} \Rightarrow x = r y$ $y^{2} (10 r^{2} - 9 r + 2) = 0$ $\Rightarrow r = \frac{2}{5} \lor r = \frac{1}{2}$ $\Rightarrow \frac{x}{y} = \frac{2}{5} \lor \frac{x}{y} = \frac{1}{2}$
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