Các câu hỏi tương tự
Cho các số thực a, b, c khác 0 thỏa mãn a + b + c = 0. CMR: \(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}=\left|\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right|\)
Cho a,b,c là các số thực khác 0 thỏa mãn a+b+c=0.CMR:
\(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}=\left|\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right|\)
1) Cho a,b,c0 tm a+b+c3. Cmr frac{1}{2+a^2+b^2}+frac{1}{2+b^2+c^2}+frac{1}{2+c^2+a^2}lefrac{3}{4}2) Cho a,b,c0 tm a^2+b^2+c^2 bé hơn hoặc bằng abc. Cmr frac{a}{a^2+bc}+frac{b}{b^2+ca}+frac{c}{c^2+ab}lefrac{1}{2}3) Cho a,b,c0 tm a+b+c3. Cmr frac{ab}{sqrt{3+c}}+frac{bc}{sqrt{3+a}}+frac{ca}{sqrt{3+b}}lefrac{3}{2}4) Cho a,b,c0 tm a+b+c2. Cmr frac{a}{sqrt{4a+3bc}}+frac{b}{sqrt{4b+3ca}}+frac{c}{sqrt{4c+3ab}}le15) Cho a,b,c0. Cmr sqrt{frac{a^3}{5a^2+left(b+cright)^2}}+sqrt{frac{b^3}{5b^2+left(c+aright)...
Đọc tiếp
1) Cho a,b,c>0 tm a+b+c=3. Cmr \(\frac{1}{2+a^2+b^2}+\frac{1}{2+b^2+c^2}+\frac{1}{2+c^2+a^2}\le\frac{3}{4}\)
2) Cho a,b,c>0 tm a^2+b^2+c^2 bé hơn hoặc bằng abc. Cmr \(\frac{a}{a^2+bc}+\frac{b}{b^2+ca}+\frac{c}{c^2+ab}\le\frac{1}{2}\)
3) Cho a,b,c>0 tm a+b+c<=3. Cmr \(\frac{ab}{\sqrt{3+c}}+\frac{bc}{\sqrt{3+a}}+\frac{ca}{\sqrt{3+b}}\le\frac{3}{2}\)
4) Cho a,b,c>0 tm a+b+c=2. Cmr \(\frac{a}{\sqrt{4a+3bc}}+\frac{b}{\sqrt{4b+3ca}}+\frac{c}{\sqrt{4c+3ab}}\le1\)
5) Cho a,b,c>0. Cmr \(\sqrt{\frac{a^3}{5a^2+\left(b+c\right)^2}}+\sqrt{\frac{b^3}{5b^2+\left(c+a\right)^2}}+\sqrt{\frac{c^3}{5c^2+\left(a+b\right)^2}}\le\sqrt{\frac{a+b+c}{3}}\)
6) Cho a,b,c>0. Cmr \(\frac{a^2}{\left(2a+b\right)\left(2a+c\right)}+\frac{b^2}{\left(2b+a\right)\left(2b+c\right)}+\frac{c^2}{\left(2c+a\right)\left(2c+b\right)}\le\frac{1}{3}\)
Giúp mình với nhé các bạn
cho a,b,c>0
CMR:
\(\left(a+b+\frac{1}{2}\right)^2+\left(b+c+\frac{1}{2}\right)^2+\left(c+a+\frac{1}{2}\right)^2\ge4\left(\frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{b}+\frac{1}{c}}+\frac{1}{\frac{1}{c}+\frac{1}{a}}\right)\)
cho a,b,c>0 . CMR :
\(\left(a+b+\frac{1}{2}\right)^2+\left(b+c+\frac{1}{2}\right)^2+\left(c+a+\frac{1}{2}\right)^2\ge4\left(\frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{b}+\frac{1}{c}}+\frac{1}{\frac{1}{c}+\frac{1}{a}}\right)\)
CMR: \(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{2\sqrt[3]{abc}}\ge\frac{\left(a+b+c+\sqrt[3]{abc}\right)^2}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\) với mọi a,b,c >0
Cho a khác b khác c và a,b,c >0 thỏa \(\left(a+c\right)\left(b+c\right)=1\) \(CMR\frac{1}{\left(a-b\right)^2}+\frac{1}{\left(a+c\right)^2}+\frac{1}{\left(b+c\right)^2}\ge4\)
Cho a + b + c = 0 và a,b,c khác 0. CMR:
\(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}=|\frac{1}{a}+\frac{1}{b}+\frac{1}{c}|\)
Cho \(a,b,c>0\)
CMR: \(\frac{1+\sqrt{3}}{3\sqrt{3}}\left(a^2+b^2+c^2\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge a+b+c+\sqrt{a^2+b^2+c^2}\)