If 2x^2 - 3xy + y^2 = 0, find the ratio of x:y.
the previous two methods given by HallsofIvy and Diagonal
are the main variations.
may be converted to a quadratic in
This is now of the form
for which the solutions are
You achieve the exact same result by writing the expression as a multiplication of factors
Two numbers multiplied give zero, hence either one of them can be zero.
which yields two solutions, x=y and 2x=y
from which the exact same ratios obtained from the quadratic may be written.