Đề câu a sai nhéhttp://toan.hoctainha.vn/Hoi-Dap/Cau-Hoi/128746/bat-dang-thuc-cauchyb,$a^3+b^3=(a+b)(a^2-ab+b^2) \geqslant (a+b)(2ab-ab)=ab(a+b)$c,$\frac{1}{a}+\frac{1}{b}\geqslant \frac{4}{a+b}$$\frac{1}{b}+\frac{1}{c}\geqslant \frac{4}{b+c}$$\frac{1}{c}+\frac{1}{a}\geqslant \frac{4}{a+c}$Cộng theo vế suy ra đpcm.
Đề câu a sai nhéhttp://toan.hoctainha.vn/Hoi-Dap/Cau-Hoi/128746/bat-dang-thuc-cauchyb,$a^3+b^3=(a+b)(a^2-ab+b^2) \geqslant (a+b)(2ab-ab)=ab(a+b)$c,$\frac{1}{a}+\frac{1}{b}\geqslant \frac{4}{a+b}$$\frac{1}{b}+\frac{1}{c}\geqslant \frac{4}{b+c}$$\frac{1}{c}+\frac{1}{a}\geqslant \frac{4}{a+c}$Cộng theo vế suy ra đpcm.d,$(1+a)(1+b)=a+b+ab+1\geqslant ab+2\sqrt{ab}+1=(\sqrt{ab}+1)^2$