Áp dụng BĐT Cauchy:
a+b \geq 2\sqrt{ab}
=> a^2+b^2+2ab \geq 4ab
=> a^2+b^2 \geq 2ab
b^2+1 \geq 2b
=> a^2+2b^2+3 \geq 2ab+2b+2
=> \dfrac{1}{a^2+2b^2+3} \leq \dfrac{1}{2}.(\dfrac{1}{ab+b+1})
CMTT: \dfrac{1}{b^2+2c^2+3} \leq \dfrac{1}{2}.(\dfrac{1}{bc+c+1})
\dfrac{1}{c^2+2a^2+3} \leq...