Bài5: cho a,b,c>0.CMR
1, 2/a+1/b >= 4/a+b
2, 1/a+1/b+1/c>= a/a+b+c
Bài 6: cho a,b>=0 cmr
1, a^3+b^4>=ab(a+b)
2, a^4+b^4>=ab(a^2+b^2)
3, a5+b5>=ab(a^3+b^3)
Bài 7 cho a,b,c>0 cmr
1/a^3+b^3+abc +1/b^3+c^3+abc+1/c^3+a^3+2 <1/abc
Bài 8cho a,b,c>0;abc=1
1, 1/a^3+b^3+2 +1/b^3+c^3+2 +1/c^3+a^3+2 =< 1
2,ab/a^5+b^5+ab +bc/b^5+c^5+bc + ca/c^5+a^5+ca =<1
a) Cho a3+b3+c3-3abc . CMR: a+b+c=0 ; a=b=c.
b) Cho a4+b4+c4+d4=4abcd và a,b,c,d >0 . CMR : a=b=c=d.
Cho a,b,c>0. CMR \(\frac{a^4}{a^3+b^3}+\frac{b^4}{b^3+c^3}+\frac{c^4}{c^3+a^3}\ge\frac{a+b+c}{2}\)
Bài 1:Cho \(a+b+c=3\) \(CMR\) \(a^4+b^4+c^4\ge a^3+b^3+c^3\)
Bài 2:Cho \(a>0;b>0;c>0\) thỏa mãn \(a^2+b^2+c^2=1\)
\(CMR\)\(\frac{1}{a^2+b^2}+\frac{1}{b^2+c^2}+\frac{1}{a^2+c^2}\le\frac{a^3+b^3+c^3}{2abc}+3\)
giup mình câu này nhé cho a+b+c=0 cmr a^5.(b^2+c^2)+b^5.(a^2+c^2)+c^5.(a^2+b^2)=1/2(a^3+b^3+c^3).(a^4+b^4+c^4)
ai nhanh 10 tick
giúp mình câu này nhé cho a+b+c=0 cmr a^5.(b^2+c^2)+b^5.(a^2+c^2)+c^5.(a^2+b^2)=1/2(a^3+b^3+c^3).(a^4+b^4+c^4)
ai đúng 10 tick
Cho a,b,c >0. CMR \(3\left(a^4+b^4+c^4\right)\ge\left(a+b+c\right)\left(a^3+b^3+c^3\right)\)
Cho a+b+c=0 CMR
\(a^5.\left(b^2+c^2\right)+b^5.\left(c^2+a^2\right)+c^5.\left(a^2+b^2\right)=\frac{1}{2}.\left(a^3+b^3+c^3\right).\left(a^4+b^4+c^4\right)\)
cho a,b,c,d > 0. CMR \(\frac{a^4}{a^3+2b^3}+\frac{b^4}{b^3+2c^3}+\frac{c^4}{c^3+2d^3}+\frac{d^4}{d^3+2a^3}\ge\frac{a+b+c+d}{3}\)
