The problem asks us to form a quadratic expression based on the diagram. The diagram shows a right-angled triangle with sides labeled $p$, $q$, and $r$, where $r$ is the hypotenuse.

GeometryPythagorean TheoremQuadratic ExpressionRight Triangle
2025/4/25

1. Problem Description

The problem asks us to form a quadratic expression based on the diagram. The diagram shows a right-angled triangle with sides labeled pp, qq, and rr, where rr is the hypotenuse.

2. Solution Steps

Since the triangle is right-angled, we can apply the Pythagorean theorem:
p2+q2=r2p^2 + q^2 = r^2
We want to express this as a quadratic expression. The general form of a quadratic expression is ax2+bx+c=0ax^2 + bx + c = 0.
Rearranging the Pythagorean theorem, we get:
r2p2q2=0r^2 - p^2 - q^2 = 0

3. Final Answer

r2p2q2=0r^2 - p^2 - q^2 = 0

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