证：a^2 - 16b^2 - c^2 + 6ab + 10bc = 0a^2 + 6ab + 9b^2 - (25b^2 - 10bc + c^2)= 0(a + 3b)^2 - (5b - c)^2 = 0(a + 3b + 5b - c)(a + 3b -5b + c）= 0（a + 8b - c)(a - 2b + c）= 0因为a、b、c是三角形三边的长,所以 a + b - c 〉0,则 a + 8b - c 〉0.要使（a + 8b - c)(a - 2b + c）= 0,必须(a - 2b + c）= 0所以 a+c=2b