a: \(=\left(x^4-4\right)+5x\left(x^2+2\right)\)
\(=\left(x^2+2\right)\left(x^2+5x-2\right)\)
b: \(x^8+x+1\)
\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
c: \(x^5+x^4+1\)
\(=x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^3-x+1\right)\)
cho x,y,z>0 thỏa mãn \(\sqrt{x}+\sqrt{y}+\sqrt{z}=1\)
Cmr: \(\sqrt{\frac{xy}{x+y+2z}}+\sqrt{\frac{yz}{y+z+2x}}+\sqrt{\frac{xz}{x+z+2y}}\le\frac{1}{2}\)
Choi x,y,z thoả mãn điều kiện xyz=144. Tìm giá trị
\(P=\frac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+12}+\frac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\frac{12\sqrt{z}}{\sqrt{xz}+12\sqrt{x}+12}\)
tìm tát cả số nguyên dương x,y,z thỏa mãn
\(x^2y+x+y-7z=yz\left(xy+1\right)\)
\(Chox,y,z>0:xy+x=1\)
Tìm GTLN:\(\dfrac{x}{x+1}+\dfrac{y}{y+1}+\dfrac{z}{z+1}\)
giải hệ phương trình
1 , \(\left\{{}\begin{matrix}\left(x+y\right)\left(x-1\right)=\left(x-y\right)\left(x+1\right)+2xy\\\left(y-x\right)\left(y-1\right)=\left(y+x\right)\left(y-2\right)-2xy\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}2\left(\frac{1}{x}+\frac{1}{2y}\right)+3\left(\frac{1}{x}-\frac{1}{2y}\right)^2=9\\\left(\frac{1}{x}+\frac{1}{2y}\right)-6\left(\frac{1}{x}-\frac{1}{2y}\right)^2=-3\end{matrix}\right.\)
3 , \(\left\{{}\begin{matrix}\frac{xy}{x+y}=\frac{2}{3}\\\frac{yz}{y+z}=\frac{6}{5}\\\frac{zx}{z+x}=\frac{3}{4}\end{matrix}\right.\)
4 , \(\left\{{}\begin{matrix}2xy-3\frac{x}{y}=15\\xy+\frac{x}{y}=15\end{matrix}\right.\)
5 , \(\left\{{}\begin{matrix}x+y+3xy=5\\x^2+y^2=1\end{matrix}\right.\)
6 , \(\left\{{}\begin{matrix}x+y+xy=11\\x^2+y^2+3\left(x+y\right)=28\end{matrix}\right.\)
7, \(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=4\\x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=4\end{matrix}\right.\)
8, \(\left\{{}\begin{matrix}x+y+xy=11\\xy\left(x+y\right)=30\end{matrix}\right.\)
9 , \(\left\{{}\begin{matrix}x^5+y^5=1\\x^9+y^9=x^4+y^4\end{matrix}\right.\)
giải phương trình nghiệm nguyên
\(\frac{xy}{z}+\frac{yz}{x}+\frac{xz}{y}=3\)
giải phương trình nghiệm nguyên
\(\left\{{}\begin{matrix}x+y+z=5\\xy+yz+xz=8\end{matrix}\right.\)
cho x,y và z là các số thực thỏa mãn \(\left\{{}\begin{matrix}x+z-yz=1\\y-3z+xz=1\end{matrix}\right.\). Tìm min \(T=x^2+y^2\)
