Các câu hỏi tương tự
a, b, c > 0. CM:
a)\(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge\sqrt{\frac{a^2+b^2}{2}}+\sqrt{\frac{b^2+c^2}{2}}+\sqrt{\frac{c^2+a^2}{2}}\)
b)\(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge\sqrt{a^2+b^2-ab}+\sqrt{b^2+c^2-bc}+\sqrt{c^2+a^2-ac}\)
Cho a,b>0. CM
\(\frac{a+b}{\sqrt{ab}}+\frac{\sqrt{ab}}{a+b}\ge\frac{5}{2}\)
1)Cho a,b>0
Cm: \(\frac{a^2+b^2}{2}+\frac{a+b}{4}\ge a\sqrt{b}+b\sqrt{a}\)a
2)Cho (a,240)=1. Cm: a^4-1 chia hết cho 240
cho a,b,c dương và a+b+c=1.CMR: \(\frac{\sqrt{\left(^{a^2+2ab}\right)}}{\sqrt{\left(b^2+2c^2\right)}}+\frac{\sqrt{\left(^{b^2+2bc}\right)}}{\sqrt{\left(c^2+2a^2\right)}}+\frac{\sqrt{\left(^{c^2+2ac}\right)}}{\sqrt{\left(a^2+2b^2\right)}}\ge\frac{1}{a^2+b^2+c^2}\)
1. Cho a0,b0. C/m frac{a}{sqrt{b}}-sqrt{a}gesqrt{b}-frac{b}{sqrt{a}}2. Cho ane0,bne0. C/m a^4+b^4lefrac{a^6}{b^2}+frac{b^6}{a^2}3. C/m frac{x^2}{y^2}+frac{y^2}{z^2}+frac{z^2}{x^2}gefrac{x}{y}+frac{y}{z}+frac{z}{x}4. C/m frac{x^2+y^2}{2}geleft(frac{x+y}{2}right)^25. forall a,b0. C/m frac{a^3}{b}+b^3a^2+ab
Đọc tiếp
1. Cho \(a>0,b>0\). C/m \(\frac{a}{\sqrt{b}}-\sqrt{a}\ge\sqrt{b}-\frac{b}{\sqrt{a}}\)
2. Cho \(a\ne0,b\ne0\). C/m \(a^4+b^4\le\frac{a^6}{b^2}+\frac{b^6}{a^2}\)
3. C/m \(\frac{x^2}{y^2}+\frac{y^2}{z^2}+\frac{z^2}{x^2}\ge\frac{x}{y}+\frac{y}{z}+\frac{z}{x}\)
4. C/m \(\frac{x^2+y^2}{2}\ge\left(\frac{x+y}{2}\right)^2\)
5. \(\forall a,b>0\). C/m \(\frac{a^3}{b}+b^3>a^2+ab\)
\(\sqrt{\frac{2}{a}}+\sqrt{\frac{2}{b}\: }+\sqrt{\frac{2}{c}}\le\sqrt{\frac{a+b}{ab}}\sqrt{\frac{b+c}{bc}}+\sqrt{\frac{c+a}{ca}}\)
Với a,b,c >0 . Cm
CM: \(\sqrt{\frac{a^2}{b}}+\sqrt{\frac{b^2}{a}}\ge\sqrt{a}+\sqrt{b}\)
Cho a, b, c > 0. CM:\(\frac{a^2b}{2a^3+b^3}+\frac{2}{3}\ge\frac{a^2+2ab}{2a^2+b^2}\)
Cho a, b, c > 0 thoả mãn :ab + bc + ca = abc.CMR:
\(\frac{\sqrt{b^2+2a^2}}{ab}+\frac{\sqrt{c^2+2b^2}}{bc}+\frac{\sqrt{a^2+2c^2}}{ca}\ge\sqrt{3}\)