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Problem 633

AMC 10/12, early questions

Geometry Difficulty 3.6 Find the answer Harvard-MIT Mathematics Tournament · United States

The graph of $x^{4}=x^{2} y^{2}$ is a union of $n$ different lines. What is the value of $n$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Solution:
The equation $x^{4}-x^{2} y^{2}=0$ factors as $x^{2}(x+y)(x-y)=0$ , so its graph is the union of the three lines $x=0$ , $x+y=0$ , and $x-y=0$ .

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