Question

solve if 5x^2-13xy+6y^2=0 then x:y is

Answer 1

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Answer is attached to the file

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Answer 2

Heyy Buddy

Here's your Answer

Given:-

5x^2 - 13xy + 6y^2 = 0.

To find :-

x : y = ?

Find :-

$5 {x}^{2} - 13xy + 6 {y}^{2} = 0 \\ \\ = > 5 {x}^{2} + 6 {y}^{2} = 13xy \\ \\ = > \frac{5 {x}^{2} }{xy} + \frac{6{y}^{2} }{xy} = 13 \\ \\ = > \frac{5x}{y} + \frac{6y}{x} = 13 \\ \\ take \: \frac{x}{y} = a \: \\ therefore \: \frac{y}{x} = \frac{1}{a} \\ \\ = > 5a + \frac{6}{a} = 13 \\ \\ = > 5 {a}^{2} + 6 = 13a \\ \\ = > 5 {a}^{2} - 13a + 6 = 0 \\ \\ = > 5 {a}^{2} + ( - 10- 3)a + 6 = 0 \\ \\ = > 5 {a}^{2} - 10a - 3a + 6 = 0 \\ \\ = > 5a(a - 2) - 3(a - 2) = 0 \\ \\ = > (a - 2) \: and \: (5a - 3) \\ \\ = > a = 2 \: and \: a = \frac{3}{5} \\ \\ now \: according \: to \: our \: supposition \\ \\ \frac{x}{y} = a = 2$
=> x : y = 2 : 1 or 3 : 5.
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