Các câu hỏi tương tự
cho a, b, c>0. CMR a\(\frac{a^3}{b}\ge a^2+ab-b^2\)
CM \(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}\ge\frac{c}{b}+\frac{b}{a}+\frac{a}{c}\)
Cho a, b, c là độ dài 3 cạnh của tam giác CM \(\frac{1}{a+b-c}+\frac{1}{b+c-a}+\frac{1}{c+a-b}\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
1. CHo frac{1}{a}+frac{1}{b}frac{2}{b}(a,b ,c 0 )CMR: frac{a+b}{2a-b}+frac{c+b}{2c-b}ge42. CHo a,b,c 0 và a2 + b2 + c2 3. CMR: a2b + b2c + c2a 33. CHo a,b,c thõa mãn a + b + c 3. CM: frac{a^2}{a+2b^3}+frac{b^2}{b+2c^3}+frac{c^2}{c+2a^3}le14. CHo a,b,c 0 thõa mãn a + b + c 3/2CM: Pleft(3+frac{1}{a}+frac{1}{b}right)left(3+frac{1}{b}+frac{1}{c}right)left(3+frac{1}{c}+frac{1}{a}right)ge343
Đọc tiếp
1. CHo \(\frac{1}{a}+\frac{1}{b}=\frac{2}{b}\)(a,b ,c >0 )
CMR: \(\frac{a+b}{2a-b}+\frac{c+b}{2c-b}\ge4\)
2. CHo a,b,c > 0 và a2 + b2 + c2 = 3. CMR: a2b + b2c + c2a < = 3
3. CHo a,b,c thõa mãn a + b + c = 3. CM: \(\frac{a^2}{a+2b^3}+\frac{b^2}{b+2c^3}+\frac{c^2}{c+2a^3}\le1\)
4. CHo a,b,c > 0 thõa mãn a + b + c < = 3/2
CM: \(P=\left(3+\frac{1}{a}+\frac{1}{b}\right)\left(3+\frac{1}{b}+\frac{1}{c}\right)\left(3+\frac{1}{c}+\frac{1}{a}\right)\ge343\)
1) Cho \(\frac{a^2}{b+c}+\frac{b^2}{a+c}+\frac{c^2}{a+b}=0\)
CM: \(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=1\)
2) Cho \(abc\ne1\)và \(\frac{ab+1}{b}=\frac{bc+1}{c}=\frac{ac+1}{a}\)
CM: a=b=c
Cho (a+b+c)^2=a^2+b^2+c^2 va a,b,c khac 0. CM :
\(\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}=\frac{3}{abc}\)
1) Cho frac{a-left(c-bright)}{b-c}+frac{b-left(a-cright)}{c-a}+frac{c-left(b-aright)}{a-b}3CM frac{a}{left(b-cright)^2}+frac{b}{left(c-aright)^2}+frac{c}{left(a-bright)^2}02) Cho frac{1}{a}+frac{1}{c}frac{1}{b-c}-frac{1}{a-b}và acne0; ane b; bne cCM frac{a}{c}frac{a-c}{b-c}
Đọc tiếp
1) Cho \(\frac{a-\left(c-b\right)}{b-c}+\frac{b-\left(a-c\right)}{c-a}+\frac{c-\left(b-a\right)}{a-b}=3\)
CM \(\frac{a}{\left(b-c\right)^2}+\frac{b}{\left(c-a\right)^2}+\frac{c}{\left(a-b\right)^2}=0\)
2) Cho \(\frac{1}{a}+\frac{1}{c}=\frac{1}{b-c}-\frac{1}{a-b}\)và \(ac\ne0\); \(a\ne b\); \(b\ne c\)
CM \(\frac{a}{c}=\frac{a-c}{b-c}\)
Cho (a+b+c)2=a2+b2+c2 và a,b,c khác 0
Cm \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{3}{abc}\)
Cho a, b, c > 0. CM:
a)\(\frac{a}{2a+b+c}+\frac{b}{a+2b+c}+\frac{c}{a+b+2c}\le\frac{3}{4}\)
b)\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge\frac{b+c}{a^2+bc}+\frac{c+a}{b^2+ac}+\frac{a+b}{c^2+ab}\)
c)\(\frac{a^2}{b^2+c^2}+\frac{b^2}{c^2+a^2}+\frac{c^2}{a^2+b^2}\ge\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\)
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CHO \(ABC\ne O\)VÀ \(\left(A+B+C\right)^2=A^2+B^2+C^2\).CM \(\frac{1}{A^3}+\frac{1}{B^3}+\frac{1}{C^3}=\frac{3}{ABC}\)
Cho a>b>c>d>0 va \(a^2+b^2+c^2=1\)
CM \(\frac{a^3}{b+c}+\frac{b^3}{a+c}+\frac{c^3}{a+b}\ge\frac{1}{2}\)