Bài 1: Căn bậc hai
Các câu hỏi tương tự
c/m bất đảng thức :
a)dfrac{a}{3b}+dfrac{bleft(a+bright)}{a^2+ab+b^2}
b)dfrac{a}{b^2}+dfrac{b}{a^2}+dfrac{16}{a+b}ge5left(dfrac{1}{a}+dfrac{1}{b}right)
c)dfrac{a}{2b}+dfrac{2b}{a+b}+dfrac{ab^2}{2left(a^3+2b^3right)}gedfrac{5}{3}
d)dfrac{a}{4b^2}+dfrac{2b}{left(a+bright)^2}gedfrac{9}{4left(a+2bright)}
e)dfrac{2}{a^2+ab+b^2}+dfrac{1}{3b^2}gedfrac{9}{left(a+2bright)^2}
Đọc tiếp
c/m bất đảng thức :
a)\(\dfrac{a}{3b}+\dfrac{b\left(a+b\right)}{a^2+ab+b^2}\)
b)\(\dfrac{a}{b^2}+\dfrac{b}{a^2}+\dfrac{16}{a+b}\ge5\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\)
c)\(\dfrac{a}{2b}+\dfrac{2b}{a+b}\)+\(\dfrac{ab^2}{2\left(a^3+2b^3\right)}\ge\dfrac{5}{3}\)
d)\(\dfrac{a}{4b^2}+\dfrac{2b}{\left(a+b\right)^2}\ge\dfrac{9}{4\left(a+2b\right)}\)
e)\(\dfrac{2}{a^2+ab+b^2}+\dfrac{1}{3b^2}\ge\dfrac{9}{\left(a+2b\right)^2}\)
Cho a,b,c>0 CMR
\( \frac{a^3}{bc}+ \frac{b^3}{ac}+ \frac{c^3}{ab}\ge \frac{3(a^2+b^2+c^2)}{a+b+c} \)
cho a\(\ge0;b\ge0\). Chứng minh
a)\(a+b\ge2\sqrt{ab}\)
b)\(\sqrt{\dfrac{a+b}{2}}\ge\dfrac{\sqrt{a}+\sqrt{2}}{2}\)
Chứng minh rằng:
a> \(\sqrt{\left(a+c\right)\left(b+d\right)}\ge\sqrt{ab}+\sqrt{cd}\) với a,b,c,d >0
b> \(\dfrac{x^2+5}{\sqrt{x^2+4}}>2\)
với mọi a,b,c ko âm
c/m \(\dfrac{3}{2}\left(a+b+c\right)\ge\sqrt{a^2+bc}+\sqrt{b^2+ca}+\sqrt{c^2+ab}\)
Cho a,b,c,d>0 và a+b+c+d=4
Chứng minh rằng \(\dfrac{1}{ab}+\dfrac{1}{cd}\ge\dfrac{a^2+b^2+c^2+d^2}{2}\)
Cho a,b,c >0.Chứng minh:
\(P=\dfrac{a^2b}{ab^2+1}+\dfrac{b^2c}{bc^2+1}+\dfrac{c^2a}{ca^2+1}\ge\dfrac{3abc}{1+abc}\)
2) Cho a,b ≥ 0 .CMR :
a) \(\dfrac{a^2+b^2}{2}\) ≥ \(\left(\dfrac{a+b}{2}\right)^2\) b) \(\dfrac{a^3+b^3}{2}\) ≥ \(\left(\dfrac{a+b}{2}\right)^3\)
Cm. A2 + B2 + C2 ≥ AB +BC+ AC