求高中不等式题目及答案答:二、解答题 4.(★★★)已知a,b,c为正实数,a+b+c=1. 求证:(1)a2+b2+c2≥ (2) ≤6 5.(★★★)已知x,y,z∈R,且x+y+z=1,x2+y2+z2= ,证明:x,y,z∈[0, ] 6.(★★★)证明下列不等式: (1)若x,y,z∈R,a,b,c∈R+,则 z2≥2(xy+yz+zx) (2)若x,y,z∈R+,且x+y+z...
已知实数ABC满足a+b+c=0,且a3+b3+c3=0,求a2017+b2017+c2017的值_百度...答:a+b=-c, (a+b)^2=c^2,a^3+b^3+c^3=(a+b)(a^2-ab+b^2)+c^3=-c(c^2-3ab)+c^3=3abc=0,a,b,c中有一个为0,且另两个互为相反数,a^2017,b^2017,c^2017中有一个为0,另两个互为相反数,他们的和=0