Question

If x and y both are positive and
(2x2 - 5y2) : xy = 1 : 3, find x : y.
​

Answer 1

Steps

1. We know that $AD=BC$ when $A:B=C:D$

2. Use 1

3. Factor

4. Find relation of x and y

5. Find x : y

Step 1

Pass

Step 2

$(2x^2-5y^2):xy=1:3$

$3(2x^2-5y^2)=xy$

$6x^2-xy-15y^2=0$

Step 3

Factor $6x^2-xy-15y^2$

$6x^2-xy-15y^2=(3x-5y)(2x+3y)$

Step 4

$(3x-5y)(2x+3y)=0$

∴$3x=5y$ or $2x=-3y$

In the question, x and y are both positive, so $2x=-3y$ is out.

$3x=5y$

$y=\frac{3}{5} x$

$x:y=1:\frac{3}{5}$

∴$x:y=5:3$