It is known that in △ ABC, trilateral a, B, C satisfy the equation A & sup2; - 16b & sup2; - C & sup2; + 6ab + 10bc = 0, and prove that a + C = 2B

It is known that in △ ABC, trilateral a, B, C satisfy the equation A & sup2; - 16b & sup2; - C & sup2; + 6ab + 10bc = 0, and prove that a + C = 2B

a²-16b²-c²+6ab+10bc=0
(a+3b)^2-(c-5b)^2=0
(a+3b+c-5b)(a+3b-c+5b)=0
(a+c-2b)(a+8b-c)=0
Triangle species a + 8b-c > 0 holds, so a + c-2b = 0
So a + C = 2B