$\left\{\begin{matrix} x^{30}+y^{4}=(x+y)^{2012}\\ y^{30}=(y^{4}+x^{2012})x^{12}\\ x,

[luugiangnam]

Giải các phương trình và hệ phương trình sau:

1)$\left\{\begin{matrix} x^{30}+y^{4}=(x+y)^{2012}\\ y^{30}=(y^{4}+x^{2012})x^{12}\\ x,y\in \mathbb{N}^{*}\\ \end{matrix}\right.$

2)$\left\{\begin{matrix} xy+\sqrt{2(x^{4}+y^{4})}=1\\ \\ x^{n+4}.y^{n}+x^{n}y^{n+4}=\frac{2}{3^{n+2}}\\ n=2k+1, k\in \mathbb{N} \end{matrix}\right.$

3)$2\sqrt{7x^{3}-11x^{2}+25x-12}=x^{2}+6x-1$

4)$\left\{\begin{matrix} \sqrt{x}+\sqrt{y}+\sqrt{z}=1\\ \frac{1}{3x+2y}+\frac{1}{3y+2z}+\frac{1}{3z+2x}=\f rac{1}{x+2y+2z}+\frac{1}{y+2x+2z}+\frac{1}{z+2x+2y } \end{matrix}\right.$

5)$\left\{\begin{matrix} 3(x+\frac{1}{x})=4(y+\frac{1}{y})=5(z+\frac{1}{z}) \\ xy+yz+zx=1 \end{matrix}\right.$

6)$\left\{\begin{matrix} (17-3x)\sqrt{5-x}+(3y-14)\sqrt{4-y}=0\\ 2\sqrt{2x+y+5}+3\sqrt{3x+2y+11}=x^{2}+6x+13 \end{matrix}\right.$

7)$(2sinx-3)(4sin^{2}x-6sinx+3)=1+3\sqrt[3]{6sinx-4}$

8)$\sqrt{\frac{x+2}{2}}-1=\sqrt[3]{3(x-3)^{2}}+\sqrt[3]{9(x-3)}$

9)$\left\{\begin{matrix} log_{2}x=2^{y+2}\\ 4\sqrt{1+x}+xy\sqrt{4+y^{2}}=0 \end{matrix}\right.$

10)$\left\{\begin{matrix} \sqrt{2x+1}+\sqrt{2y+1}=\frac{(x-y)^{2}}{2}\\ (x+y)(x+2y)+3x+2y=4 \end{matrix}\right.$

11)$\left\{\begin{matrix} 3^{x-1}.4^{\frac{y+1}{y}}=24\\ 3^{y-1}.4^{\frac{x+1}{x}}=24 \end{matrix}\right.$

12)$\left\{\begin{matrix} xyz=1\\ \frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{1}{x^{2}}+3= 2(x+y+z)\\ x,y,z\in \mathbb{R}^{+} \end{matrix}\right.$

13)$\left\{\begin{matrix} x^{2}+y^{2}+z^{2}+xyz=4\\ xy+yz+zx-xyz=2\\ x,y,z\in \mathbb{R}^{+} \end{matrix}\right.$

14)$\left\{\begin{matrix} xyz=1\\ x^{2}+y^{2}+z^{2}+x+y+z=2(xy+yz+xz)\\ x,y,z\in \mathbb{R}^{+} \end{matrix}\right.$

15)$\left\{\begin{matrix} xy+yz+zx+xyz=4\\ x+y+z=xy+yz+zx\\ x,y,z\in \mathbb{R}^{+} \end{matrix}\right.$
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