# High School Challenge 3

Algebra Level 3

In the equation $$(x-y)(x-z)$$, $$y$$ and $$z$$ are the shorter sides of a right-angled triangle where $$x$$ is a real number and the hypotenuse is of length $$\sqrt{b^{2}+2bc}$$ . If $$(x-y)(x-z) = x^{2}+bx+c$$ (where b and c are real numbers), find $$\frac{y(y-1)}{z(z-1)}$$.

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