\(\Leftrightarrow4\left(a^3+b^3\right)-\left(a+b\right)^3\ge0\)
\(\Leftrightarrow4a^3+4b^3-a^3-3a^2b-3ab^2-b^3\ge0\)
\(\Leftrightarrow a^3+b^3-a^2b-ab^2\ge0\)
\(\Leftrightarrow a^2\left(a-b\right)+b^2\left(b-a\right)\ge0\)
\(\Leftrightarrow\left(a-b\right)\left(a^2-b^2\right)\ge0\)
\(\Leftrightarrow\left(a-b\right)^2\left(a+b\right)\ge0\)(luôn đúng)
\(\Rightarrowđpcm\)
CMR: \(8\left(a^3+b^3+c^3\right)\ge\left(a+b\right)^3+\left(b+c\right)^3+\left(c+a\right)^3\) với a, b, c > 0
CMR: \(2\left(a^3+b^3\right)\) ≥ \(\left(a+b\right)\left(a^2+b^2\right)\) với a, b > 0
CMR: \(\left(a+b\right)\left(a^3+b^3\right)\le2\left(a^4+b^4\right)\)
Cho a, b, c > 0 . CMR:
\(\frac{1}{a+b+c}\ge\frac{a^3}{\left(2a^2+b^2\right)\left(2a^2+c^2\right)}+\frac{b^3}{\left(2b^2+c^2\right)\left(2b^2+a^2\right)}+\frac{c^3}{\left(2c^2+a^2\right)\left(2c^2+a^2\right)}\)
CMR: \(\left(a+b\right)\left(a^3+b^3\right)\) ≤ \(2\left(a^4+b^4\right)\)
Cho a,b,c khác 0 thỏa mãn \(\left(1+\dfrac{b}{a}\right)\left(1+\dfrac{c}{b}\right)\left(1+\dfrac{a}{c}\right)=8\)
CMR \(\dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}=\dfrac{3}{4}+\dfrac{ab}{\left(a+b\right)\left(b+c\right)}+\dfrac{bc}{\left(b+c\right)\left(c+a\right)}+\dfrac{ca}{\left(c+a\right)\left(a+b\right)}\)
CMR: \(\left(a^2+b^2\right)\left(a^4+b^4\right)\) ≥ \(\left(a^3+b^3\right)^2\)
CMR: \(\left(a^3+b^3+c^3\right)\ge a^3+b^3+c^3+24abc\) với a, b, c ≥ 0
Cho \(a,b,c>0\) và \(a+b+c=3\). CMR : \(P=\dfrac{a^3}{b\left(2c+a\right)}+\dfrac{b^3}{c\left(2a+b\right)}+\dfrac{c^3}{a\left(2b+c\right)}\ge1\)
giúp nha mn :==|_T-T
