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Durkein

Durkein

Đăng ký: 30-12-2018
Offline Đăng nhập: 16-01-2019 - 23:19
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$\frac{x-3x^2}{2}+\sqrt{2x^4-x^3+7x^2-3x+3...

03-01-2019 - 20:06

Giải các phương trình sau:
 

1) $x+\sqrt{4-x^2}=2+3x\sqrt{4-x^2}$

 

2) $\sqrt[3]{81x-8}=x^3-2x^2+\frac{4}{3}x-2$

 

3) $7x^2+7x=\sqrt{\frac{4x+9}{28}}$, với $x> 0$

 

4) $x^2+\sqrt{2-x}=2x^2\sqrt{2-x}$

 

5) $\frac{\sqrt{x^3+1}}{x^2+2}=\frac{2}{5}$

 

6) $\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+14}=4-2x-x^2$

 

7) $\sqrt{x^2-x+19}+\sqrt{7x^2+8x+13}+\sqrt{13x^2+17x+7}=3\sqrt{3}(x+2)$

 

8) $2\sqrt[4]{27x^2+24x+\frac{28}{3}}=1+\sqrt{\frac{27}{2}x+6}$

 

9) $\frac{x-3x^2}{2}+\sqrt{2x^4-x^3+7x^2-3x+3}=2$

 

10) $\sqrt{2-x^2}+\sqrt{2-\frac{1}{x^2}}=4-(x+\frac{1}{x})$


$\left\{\begin{matrix} x^{2} + xy + 2y = 2...

31-12-2018 - 10:19

Giải các hệ phương trình sau:

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

 

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

 

3) $\left\{\begin{matrix} 1 + x^{3}y^{3} = 19x^{3} \\ y + xy^{2} = -6x^{2} \end{matrix}\right.$

 

4) $\left\{\begin{matrix} \sqrt{3x}(1+\frac{1}{x+y}) = 2 \\ \sqrt{7y}(1-\frac{1}{x+y}) = 4\sqrt{2} \end{matrix}\right.$

 

5) $\left\{\begin{matrix} x^{2} + y^{2} + xy + 1 = 4y \\ y(x+y)^{2} = 2x^{2} + 7y + 2 \end{matrix}\right.$

 

6) $\left\{\begin{matrix} y+xy^{2}=6x^{2} \\ 1+x^{2}y^{2}=5x^{2} \end{matrix}\right.$

 

7) $\left\{\begin{matrix} (x+y)(1+\frac{1}{xy})=5 \\ (x^{2}+y^{2})(1+\frac{1}{x^{2}y^{2}})=49 \end{matrix}\right.$

 

8) $\left\{\begin{matrix} x^{2}+y+x^{3}y+xy^{2}+xy=-\frac{5}{4} \\ x^{4}+y^{2}+xy(1+2x)=-\frac{5}{4} \end{matrix}\right.$

 

9) $\left\{\begin{matrix} \sqrt{7x+y} + \sqrt{2x+y} = 5 \\ \sqrt{2x+y}+x-y=2 \end{matrix}\right.$

 

10) $\left\{\begin{matrix} (4x^{2}+1)x+(y-3)\sqrt{5-2y}=0 \\ 4x^{2}+y^{2}+2\sqrt{3-4x}=7 \end{matrix}\right.$