\(P=\dfrac{\left(\dfrac{1}{4}\right)^2}{x}+\dfrac{\left(\dfrac{1}{2}\right)^2}{y}+\dfrac{1}{z}\ge\dfrac{\left(\dfrac{1}{4}+\dfrac{1}{2}+1\right)^2}{x+y+z}=\dfrac{49}{16}\)
Dấu "=" xảy ra khi \(\left(x;y;z\right)=\left(\dfrac{1}{7};\dfrac{2}{7};\dfrac{4}{7}\right)\)
1.Cho\(\left\{{}\begin{matrix}a,b,c>0\\a+2b+3c=20\end{matrix}\right.\)Tìm GTNN
P=\(2a+3b+4c+\dfrac{3}{a}+\dfrac{9}{2b}+\dfrac{4}{c}\)
cho x,y,z,a là các số dương;\(a^2=b+4028và\left\{{}\begin{matrix}x+y+z=a\\x^2+y^2+z^2=b\end{matrix}\right.\).tính:
S=\(x\sqrt{\dfrac{\left(2014+y^2\right)\left(2014+z^2\right)}{2014+x^2}}\)+\(y\sqrt{\dfrac{\left(2014+z^2\right)\left(2014+x^2\right)}{2014+y^2}}\)+z\(\sqrt{\dfrac{\left(2014+x^2\right)\left(2014+y^2\right)}{2014+z^2}}\)
Giải hệ phương trình
\(\left\{{}\begin{matrix}x^4+y^2=\dfrac{697}{81}\\x^2+y^2+xy-3x-4y+4=0\end{matrix}\right.\)
cm nếu \(\dfrac{x^2-yz}{x.\left(1-yz\right)}=\dfrac{y^2-xz}{y.\left(1-xz\right)}\),x≠y, xz≠1, yz≠1, x,y,z≠0 thì \(x+y+z=\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}\)
1.\(\left\{{}\begin{matrix}a,b>0\\2a+3b=4\end{matrix}\right.\)Tìm GTNN của
M=\(\dfrac{2002}{a}+\dfrac{2017}{b}+2096a-5501b\)
tìm x,y,z biết
\(\sqrt{x+1}+\sqrt{y-3}+\sqrt{z-1}=\dfrac{1}{2}\left(x+y+z\right)\)
Cho 3 số dương x,y,z thỏa mãn :
\(x\sqrt{x}+y\sqrt{y}+z\sqrt{z}=3\sqrt{xyz}\) . Tính giá trị biểu thức:
A=\(\left(1+\dfrac{\sqrt{x}}{\sqrt{y}}\right)\left(1+\dfrac{\sqrt{y}}{\sqrt{z}}\right)\left(1+\dfrac{\sqrt{z}}{\sqrt{x}}\right)\)
Giải hpt:
\(\left\{{}\begin{matrix}x^2+y^2+xy+1=4y\\y\left(x+y\right)^2=2x^2+7y+2\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x+y+z=0,35\\106x+100y+138z=41,3\end{matrix}\right.\)
