Question

（1)已知实数a 、b满足 a^2+4b^2-2a+4b+2=0,求a^2+b^2的值

Answer 1

(1)a^2+4b^2-2a+4b+2 = a^2-2a+1 + 4b^2+ 4b+1 = (a-1)^2 + (2b+1)^2=0

a-1=0,2b+1=0,a=1,b=-1/2,

a^2+b^2 = 1+(-1/2)^2 = 5/4

(2) b^2-a^2+2ac-c^2 = b^2 - (a-c)^2 = (b+a-c)(b-a+c)

根据三角形三边的关系,a+b>c,b+c>a,

知道 b^2-a^2+2ac-c^2 = (b+a-c)(b+c-a) >0