phần b)nè bạn
đặt x=a^2 + 2bc, y=b^2 + 2ac, z=c^2 + 2ab
=> x + y + z = (a + b + c)^2 <(=) 1
VT bpt : 1/x + 1/y + 1/z >(=) 3.căn3(1/xyz)...dùng cô-si cho 3 số nhé
mà x + y + z >(=) 3.căn3(xyz) <(=) 1
<=> 1/( 3.căn3 (xyz) >(=) 1 (ở đây là đổi chiều bđt)
<=> 1/ căn3 (xyz) >(=) 3
=> VT: 1/x + 1/y + 1/z >(=) 3.3 = 9
Cho ba số a,b,c dương abc=1. CMR
P = \(\dfrac{a^2}{\left(2ab+1\right)\left(ab+2\right)}+\dfrac{b^2}{\left(2bc+1\right)\left(bc+2\right)}+\dfrac{c^2}{\left(2ac+1\right)\left(ac+2\right)}\)\(\ge\)\(\dfrac{1}{3}\)
Cho a,b,c là ba số thực dương thỏa mãn abc=1.CMR
\(\dfrac{a^2}{\left(ab+2\right)\left(2ab+1\right)}+\dfrac{b^2}{\left(bc+2\right)\left(2bc+1\right)}+\dfrac{c^2}{\left(ca+2\right)\left(2ca+1\right)}\)\(\ge\)\(\dfrac{1}{3}\)
B1. Cho a, b, c là số dương. CMR:
\(\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}\ge\dfrac{a+b+c}{2}\)
B2. Cho a,b,c > 0 và a+b+c=1. cmr
\(\left(1+\dfrac{1}{a}\right)\left(1+\dfrac{1}{b}\right)\left(1+\dfrac{1}{c}\right)\ge64\)
help me!! cần gấp
a)Cho 0 < c ; c < b ; b < a . CMR:\(\sqrt{c\left(a-c\right)}+\sqrt{b\left(b-c\right)}\le\sqrt{ab}\)
b)Cho \(x\ge1;y\ge1\). CMR:\(\dfrac{1}{1+x^2}+\dfrac{1}{1+y^2}\ge\dfrac{2}{1+xy}\)
cho a,b,c là các số thực tùy ý .cmr \(\dfrac{ab}{c^2}+\dfrac{bc}{a^2}+\dfrac{ca}{b^2}\ge\) \(\dfrac{1}{2}\left(\dfrac{a+b}{c}+\dfrac{b+c}{a}+\dfrac{c+a}{b}\right)\)
Cho a,b,c là các số thực dương CMR : \(\dfrac{a}{\left(b+c\right)^2}+\dfrac{b}{\left(c+a\right)^2}+\dfrac{c}{\left(a+b\right)^2}\ge\dfrac{9}{4\left(a+b+c\right)}\)
Cho a,b,c>0 thỏa mãn a+b+c=3 CMR:
\(\dfrac{a^4}{\left(a+2\right)\left(b+2\right)}+\dfrac{b^4}{\left(b+2\right)\left(c+2\right)}+\dfrac{c^4}{\left(c+2\right)\left(a+2\right)}\ge\dfrac{1}{3}\)
Cho \(a+b=1;a\ge0;b\ge0\)
CMR:\(\left(a+\dfrac{1}{b}\right)^2+\left(b+\dfrac{1}{a}\right)^2\ge\dfrac{25}{2}\)
Cho a, b,c dương. cmr: \(\dfrac{a^3}{2b+3c}+\dfrac{b^3}{2c+3a}+\dfrac{c^3}{2a+3b}\ge\dfrac{1}{5}\left(a^2+b^2+c^2\right)\)