Answer:
4 : 7
Explanation:
First, you can start by moving all the terms to one side:
14x^2 + 6xy - 8y^2 = 0
Now we can start to factor this equation in order to find the ratio. We can start by factoring out the GCF, which is 2:
2(7x^2 + 3xy - 4y^2) = 0
In order to factor this equation we multiply the coefficients in front of the x^2 and y^2 term to get: 7 * -4 or -28. We are looking for numbers that have a product of -28 and a sum of 3(as the coefficient of the xy term). These two numbers are 7 and -4. We can rewrite the equation as:
2(7x^2 + 7xy - 4xy - 4y^2) = 0
Now, we can start to factor by grouping:
2( 7x[x + y] - 4y[x + y] ) = 0
And we can factor out [x + y]:
2(x + y)(7x - 4y) = 0
So, we can use the zero product property to get two equations:
x + y = 0
and
7x - 4y = 0
You get:
x = -y
and
7x = 4y
We can get cancel out the first solution because both x and y have to be positive. Rearranging the second equation we can get x : y = 4 : 7