Mathsphysic

2, a^(m+n)+b^(m+n)>= 1/2*(a^m+b^m)(a^n+b^n)

do đó a^10+b^10>=1/2*(a^4+b^4)(a^6+b^6)>=1/4*(a^2+b^2)^2(a^6+b^6) => đpcm

1,BĐT Holder

$$$\left ( a^{4}+b^{4}+b^{4} \right )\left ( 1+1+1 \right )\left ( 1+1+1 \right )\left ( 1+1+1 \right )\geq \left ( a+b+b \right )^{4}$$$

tương tự ta có đpcm