Иррациональные уравнения

1. $\sqrt{2x+3}+\sqrt{x-2}=\sqrt{3x+7}$
2. $22x^2+10x=\sqrt{1276x^3+364x^2}$
3.  $\sqrt{x^4-2x-5}=1-x$
4. $\sqrt{x+1}-\sqrt{4x-3}=1$
5. $\frac{1}{2}-x^2=\sqrt{\frac{1}{2}-x}$
6. $\sqrt{1+x^2}+\sqrt{1+x^2-x\sqrt{3}}=\sqrt{3}$
7. $\sqrt{x}+\sqrt{x(x+2)}-\sqrt{(x+1)^3}=0$
8. $\sqrt[5]{32x^2-32}+\sqrt[5]{(x+1)^2}+\sqrt[5]{x^2-2x+1}=0$
9. $\sqrt[3]{(x+1)^2}-\sqrt[3]{x^2+5x+6}=\sqrt[3]{x^2+4x+3}-\sqrt[3]{x^2+3x+2}$
10. $x\sqrt{y-1}+y\sqrt{x-1}=xy$
11. $\sqrt{x^2+5x+4}-\sqrt{x^2-x-6}=-\sqrt{2x^2+4x-2}$
12. $\frac{\sqrt[3]{7-x}-\sqrt[3]{x-5}}{\sqrt[3]{7-x}+\sqrt[3]{x-5}}=6-x$
13. $x^2+x+2=\frac{4}{\sqrt{3}}x\sqrt{x+2}$
14. $\sqrt{1-x^2}=4x^3-3x$
15. $\frac{1}{x}+\frac{1}{\sqrt{1-x^2}}=\frac{35}{12}$
16. $\sqrt{3x^2-1}+\sqrt{x^2-x+1}=\sqrt{3x^2+2x+1}+\sqrt{x^2+2x+4}$
17. $\sqrt{(x+2)(2x-1)}-3\sqrt{x+6}=4-\sqrt{(x+6)(2x-1)}+3\sqrt{x+2}$
18. $\sqrt{x^2-4x+4}-\sqrt{x^2+2x+1}=3$
19. $3\sqrt{x^2-4x+4}-4-x=(\sqrt{-x^2+x+2})^2$
20. $\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}=2$

Ответы

1. 3
2. 0; 2
3. $-\sqrt{3}$
4. 7/9
5. $(\sqrt{3}-1)/2$
6. $\sqrt{3}/3$
7. $(\sqrt{5}-1)/2$
8. 0
9. -3/2
10. (2; 2)
11. -4
12. 5; 6; 7
13. 1; $(3+\sqrt{33})/2$
14. $-\sqrt{2}/2; -\sqrt{2-\sqrt{2}}/2; \sqrt{2+\sqrt{2}}/2$
15. 4/5; 3/5; $-(5+\sqrt{73})/14$
16. -1
17. 7
18. $(-\infty; -1]$
19. 0
20. [1; 2]