\(\sqrt{a}.\sqrt{a}-\sqrt{b}\sqrt{b}-\sqrt{c}\sqrt{c}\)
\(=\sqrt{a^2}-\sqrt{b^2}-\sqrt{c^2}\)
\(=a-b-c\)
\(\sqrt{a}.\sqrt{a}-\sqrt{b}\sqrt{b}-\sqrt{c}\sqrt{c}\)
\(=\sqrt{a^2}-\sqrt{b^2}-\sqrt{c^2}\)
\(=a-b-c\)
Cho a,b,c>0 và\(a+b+c=\sqrt{a}+\sqrt{b}+\sqrt{c}=2\)Tính\(A=\frac{1+a}{\sqrt{a}+\sqrt{b}}+\frac{1+b}{\sqrt{b}+\sqrt{c}}+\frac{1+c}{\sqrt{c}+\sqrt{a}}\)
Cho a,bc>0 và a+b+c=\(\sqrt{a}+\sqrt{b}+\sqrt{c}=2\)Tính M=\(\frac{1+a}{\sqrt{a}+\sqrt{b}}\)+\(\frac{1+b}{\sqrt{b}+\sqrt{c}}\)+\(\frac{c+1}{\sqrt{a}+\sqrt{c}}\)
Cho các số a, b, c > 0 và a + b + c = 21. Tìm GTLN của:
a, \(\sqrt{a+2}+\sqrt{b+2}+\sqrt{c+2}\le9\)
b, \(\sqrt{a+b+2}+\sqrt{b+c+2}+\sqrt{c+a+2}\le12\)
a, b, c > 0; a + b + c = 1. CM: \(\sqrt{a+bc}+\sqrt{b+ca}+\sqrt{c+ab}\ge1+\sqrt{ab}+\sqrt{bc}+\sqrt{ca}\)
Cho a,b,c không âm thỏa mãn : a+b+c =1
CMR : a)\(\sqrt{a+1}+\sqrt{b+1}+\sqrt{c+1}< 3,5\)
b)\(\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a}\le\sqrt{6}\)
a, b, c > 0; a + b + c = 1. CM: \(\sqrt{a+bc}+\sqrt{b+ca}+\sqrt{c+ab}\ge1+\sqrt{ab}+\sqrt{bc}+\sqrt{ca}\)
\(\sqrt{\frac{2}{a}}+\sqrt{\frac{2}{b}\: }+\sqrt{\frac{2}{c}}\le\sqrt{\frac{a+b}{ab}}\sqrt{\frac{b+c}{bc}}+\sqrt{\frac{c+a}{ca}}\)
Với a,b,c >0 . Cm
Cho a,b,c>0 và \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\)
CMR \(\sqrt{a+bc}+\sqrt{b+ca}+\sqrt{c+ab}\ge\sqrt{a}+\sqrt{b}+\sqrt{c}+\sqrt{abc}\)
Cho a,b,c\(\ge0\)thỏa mãn\(a+b+c=1\)
a)Tìm max A=\(\sqrt{2a^2+a+1}+\sqrt{2b^2+b+1}+\sqrt{2c^2+c+1}\)
b)Tìm min,max B=\(\sqrt{3a+1}+\sqrt{3b+1}+\sqrt{3c+1}\)
c)Tìm min,max C=\(\sqrt{a+b}+\sqrt{b+c}+\sqrt{a+c}\)