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Cho a,b,c là các số khác 0 thỏa a+b+c=0.Cmr:
\(\dfrac{a^4}{a^4-\left(b^2-c^2\right)^2}+\dfrac{b^4}{b^4-\left(c^2-a^2\right)^2}+\dfrac{c^4}{c^4-\left(a^2-b^2\right)^2}=\dfrac{3}{4}\)
cho a, b, c > 0 cmr a^2/(b^2+c^2) + b^2/(c^2+a^2) + c^2/(a^2+b^2) >= a/(b+c) + b/(c+a) + c/(a+b)
cho a+b+c=0 cmr 4(a^7 + b^7 + c^7 ) = 7abc(a^2 + b^2 + c^2 ) ^2 .
cho a,b,c>0 cmr a^2/(b+c-a) + b^2/(c+a-b)+c^2/(a+b-c) >= a+b+c
Cho a,b,c>0. CMR: \(\frac{a^4}{\left(a+b\right)\left(a^2+b^2\right)}+\frac{b^4}{\left(b+c\right)\left(b^2+c^2\right)}+\frac{c^4}{\left(c+a\right)\left(c^2+a^2\right)}\ge\frac{a+b+c}{4}\)
cho a,b,c>0.CMR: 4/a+5/b+3/c>=4(3/a+b+2/b+c+1/c+a)
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; a+b+c=4. CMR: ∜a+∜b+∜c>2√2
Cho a,b,c>0 và a^2 + b^2 + c^2 = 3. CMR a/b + b/c + c/a >= 9/a+b+c