Question

If (6x2 - xy) : (2xy + y2) = 6 : 1, find x : y.​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

$\large{\underline{\boxed{\sf x:y = 2:3 \: \: or \: \: 3:2}}}$

Step-by-step explanation:

Given that;

(6x² - xy) : (2xy + y²) = 6 : 1

We can write it as ;

$\sf \frac{(6x {}^{2} - xy) }{(2xy + y {}^{2}) } = \frac{6}{1} \\ \\ \bf on \: cross \: multiplying : \\ \\ \sf \implies 6x {}^{2} - xy = 6(2xy + {y}^{2} ) \\ \\ \sf \implies 6x {}^{2} - xy = 12xy + 6y {}^{2} \\ \\\sf \implies 6x {}^{2} + 6y {}^{2} - xy - 12xy = 0 \\ \\ \sf \implies 6x {}^{2} - 13xy + 6y {}^{2} = 0 \\ \\ \sf \implies6x {}^{2} - 9xy - 4xy + 6y {}^{2} = 0\\ \\ \sf \implies 2x(3x - 2y) - 3y(3x - 2y) = 0 \\ \\ \sf \implies (3x - 2y)(2x - 3y) = 0$

Thus,

$\sf \implies 3x = 2y \: \: or \: \: 2x = 3y \\ \\ \sf \implies \frac{x}{y} = \frac{2}{3} \: \: or \: \: \frac{x}{y} = \frac{3}{2}$

Hence, the ratio of x : y = 2 : 3 or 3 : 2