25. Let $a, b$ and $c$ be the lengths of the three sides of a triangle. Suppose $a$ and $b$ are the roots of the equation
$$
x^{2}+4(c+2)=(c+4) x,
$$
and the largest angle of the triangle is $x^{\circ}$. Find the value of $x$.
25. Ans: 90
Since $a, b$ are the roots of the equation $x^{2}-(c+4) x+4(c+2)=0$, it follows that
$$
a+b=c+4 \quad \text { and } \quad \mathrm{ab}=4(\mathrm{c}+2) .
$$

Then $a^{2}+b^{2}=(a+b)^{2}-2 a b=(c+4)^{2}-8(c+2) \Longrightarrow a^{2}+b^{2}=c^{2}$. Hence the triangle is right-angled, and $x=90$.