If x2 + 9y2 − 6xy = 0, then x : y is equal to:

The correct answer is Option (3) → 3 : 1

The left side is a perfect square: \(x^2-6xy+9y^2\) has the form \(a^2-2ab+b^2=(a-b)^2\) with \(a=x\) and \(b=3y\).

• \(x^2-6xy+9y^2=(x-3y)^2=0\)

• A square is zero only when the number itself is zero, so \(x-3y=0\)

• \(x=3y\), so \(\displaystyle \frac{x}{y}=\frac{3}{1}\), that is, x : y = 3 : 1

Tip: Read the ratio in the order asked. From \(x=3y\), x : y is 3 : 1, while y : x would be 1 : 3, which is Option (2).