a^3 + b^3 + 3abc - c^3 / (a+b)^2 - c^2 rut gon phan thuc dai so
cho a^3+b^3+c^3=3abc va a+b+c khac 0 . tinh gia tri bieu thuc N=\(\frac{a^2+b^2+c^2}{\left(a+b+c\right)^2}\)
Cho (a+b+c)^2 = 3(ab+bc+ca). CMR: a=b=c
Cho a^3+b^3+c^3 = 3abc. CMR: a=b=c và a+b+c=0
Cho a+b+c=0. CMR: a^3+b^3+c^3 = 3abc
Bai 1:cho a,b,c la do dai 3 canh tam giac
CMR a^2016/b+c-a + b^2016/c+a-b + c^2016/a+b-c >= a^2015 +b^2015+c^2015
Bai 2;cho a,b,c la cac so thuc thoa man:0<=a,b,c<=4 va a+b+c=6
tim GTLN P=a^2+b^2+c^2 +ab+bc+ca
cho a,b,c khác 0 thỏa mãn:a+b-c=6.Tính C=a^3+b^3-c^3+3abc/(a-b)^2+(b+c)^2+(c+a)^2
Cho a+b+c=0, cm a)a^3+b^3+c^3=3abc
b) a^2+b^2+c^2=2(a^4+b^4+c^4)
Cho a^2+b^2+c^2+3= 2(a+b+c). Chứng minh a=b=c=1
2. Chứng minh rằng nếu a+b+c=0 thì a^3+b^3+c^3=3abc
cho 3 so a,b,c khac 0 va (a+b+c)^2=a^2+b^2+c^2 . chung minh \(\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}=3abc\)
Bài 1: CMR
a/ 2*(a^3+ b^3+ c^3- 3abc)=(a+b+c)*((a-b)^2+(b-c)^2+(c-a)^2)
b/ (a+b)*(b+c)*(c+a)+4abc=c*(a+b)^2+a*(b+c)^2+b*(c+a)^2
c/ (a+b+c)^3=a^3+b^3+c^3+3*(a+b)*(b+c)*(c+a)
Bài 2: Cho a+b+c=4m.CMR:
a/ 2ab+ a^2+ b^2- c^2=16m^2- 8mc
b/ (a+b-c/2)^2+(a-b+c/2)^2+(b+c-a/2)^2=a^2+b^2+c^2-4m^2