江苏涟水县涟城中学黄树兵同志来信询问如下四题的解法,现解答如下,供参考. 原题为: 1.若a、b、c表示一个三角形的三条边,并且等式cd-5d=lg(a~2+b~2-6a-8b+26)不论d取何值时,此式均能成立,求此三角形的最大角的度数. 2.k≠0,试证抛物线y=kx~2-(2k+1)x+k+2恒过一个点,并求此点坐标. 3.已知方程组 x+y=5 3x~2+y~2=23的两组解为 Comrade Huang Shubing of Licheng Middle School in Yishui County, Jiangsu Province wrote a letter asking the following four questions to be solved. The following answers are provided for reference. The original questions are: 1. If a, b, c represent the three sides of a triangle, and the equation is cd-5d= Lg(a~2+b~2-6a-8b+26) Regardless of the value of d, this formula holds. Find the maximum angle of the triangle. 2.k≠0, test parabola y=kx ~2-(2k+1)x+k+2 Constant one point, and find the coordinates of this point. 3. The two sets of solutions for the known system of equations x+y=5 3x~2+y~2=23 are