$\dfrac{a^n}{b+c}+\dfrac{b^n}{c+a}+\dfrac{c^n}{a+b} \geq \dfrac{3}{2} . \dfrac{a^n+b^n+c^n}{a+b+c}$
Bài 2: Cho $a,b,c>0$. CMR:
$3(a^3+b^3+c^3)+2abc \geq 11\sqrt{\left(\dfrac{a^2+b^2+c^2}{3}\right)^3}$
Bài 3: Cho $a,b,c>0$. CMR:
$6(a+b+c)(a^2+b^2+c^2) \leq 27abc+10\sqrt{(a^2+b^2+c^2)^3} $
Bài 4: Cho $a,b,c>0$. CMR:
$\dfrac{\sqrt{2(a^2+b^2)(b^2+c^2)(c^2+a^2)}}{abc}+\dfrac{4(ab+bc+ca)}{a^2+b^2+c^2} \geq 8$
Bài 5: Cho $ \left\{\begin{array}{l}a,b,c \in R \\ a+b+c=3 \end{array}\right. $. CMR: $(3+2a^2)(3+2b^2)(3+2c^2) \geq 125$.
Bài 6: Cho $a,b,c \geq 0$. CMR:
$\dfrac{a^3+b^3+c^3}{(a+b+c)^3}+\dfrac{10abc}{9(a+b)(b+c)(c+a)} \geq \dfrac{1}{4}$
Bài 7: Cho $a,b,c>0$. CMR:
$\dfrac{a}{(b+c)^n}+\dfrac{b}{(c+a)^n}+\dfrac{c}{(a+b)^n} \geq \left(\dfrac{3}{2}\right)^n . \dfrac{1}{(a+b+c)^{n-1}}$
Bài 8: Cho $a,b,c>0$ thỏa mãn $a+b+c=3$. CMR:
$\sqrt{\dfrac{a^3}{a^2+5b^2}}+\sqrt{\dfrac{b^3}{b^2+5c^2}}+\sqrt{\dfrac{c^3}{c^2+5a^2}} \geq \sqrt{\dfrac{3}{2}}$
Bài viết đã được chỉnh sửa nội dung bởi GaoHu_F: 13-09-2011 - 17:44