1) Chứng minh rằng: a)2(a^10+b^10) \geq (a^4+b^4)(a^6+b^6)
2)(a+b)(a^5+b^5) \geq (a^4+b^4)(a^2+b^2)
3) cho a,b,c \in [0,1]. Cmr:
a^2+b^2+c^2 \leq 1+a^2.b+b^2.c+c^2.a
4)
x,y,z \in R. Cmr:
\sqrt{x^2+xy+y^2}+\sqrt{y^2+yz+z^2}+\sqrt{x^2+zx+x^2}\geq \sqrt{3(x+y+z)}