Question

Find the value of the ratio x over y if the equation is 5x²-13xy+8y²=0 ​

Answer 1

`(x)/(y) = (8)/(5)`

Explanation:

Given

`5x^2 - 13xy + 8y^2 = 0`

Required

Find x/y

`5x^2 - 13xy + 8y^2 = 0`

Expand

`5x^2 -5xy - 8xy + 8y^2 = 0`

Factorize:

`5x(x - y) - 8y(x - y) = 0`

Factor out x - y

`(5x - 8y)(x - y) = 0`

Divide both sides by
`(x-y)`

`5x - 8y = 0`

Add 8y to both sides

`5x = 8y`

Divide both sides by 5

`x = (8)/(5)y`

Divide both sides by y

`(x)/(y) = (8)/(5)`