Иррациональные уравнения 

Часть 2

1. \(\frac{4x^2+x+1}{4|x|}=\sqrt{x+1}\)
2.  \(2(2-x^2-x)=\sqrt{1-x^2}(3x^2-6x+4)\)
3. \(\sqrt[3]{x}+\sqrt[3]{\frac{x-1}{2}}=1\)
4. \(\sqrt[3]{\frac{2+x}{x}}-\sqrt[3]{\frac{2-6x}{x}}=1\)
5. \(\sqrt[3]{5x+7}-\sqrt[3]{5x-12}=1\)
6. \(x+\sqrt{3+\sqrt{x}}=3\)
7. \(7x-5|x-1|=7\sqrt{2x+8}-5|\sqrt{2x+8}-1|\)
8. \(\sqrt{\lg x}+\sqrt{1-x^2}+\sqrt{1-y^2}=1+|\sin y|\)
9. \((1+\frac{1}{\sqrt{x}})(1+\frac{1}{\sqrt{2-x}})(\sqrt{x}+\sqrt{2-x})=8\)
10. \(x(x-2)+\sqrt{1+16x^{-2}}=\sqrt{9-2x}\)
11. \(\sqrt{x^2+x-1}+\sqrt{x-x^2+1}=x^2-x+2\)
12. \(\sqrt{x(2x+3)}+\frac{1}{x}\sqrt{1+x^2\cdot\sqrt{2}}=\sqrt{3\sqrt{2}+3x}\)
13. \(2\sqrt{x-1}+5x=\sqrt{(x^2+4)(x+24)}\)
14. \(x\sqrt{1+x}+\sqrt{3-x}=2\sqrt{1+x^2}\)
15. \(\sqrt{1-x}=2x^2-1+2x\sqrt{1-x^2}\)
16. \(\sqrt[4]{97-x}+\sqrt[4]{x}=5\)

Ответы

1. \((1\pm\sqrt{17})/8\)
2. 0; 1; \(\pm 2\sqrt{2}/3\)
3. 1
4. -1; 2/7
5. -3; 4
6. 1
7. 4
8. (1; 0)
9. 1
10. 2
11. 1
12. нет корней
13. 5
14. 1; \(1+\sqrt{2}\)
15. \(\sqrt{10-2\sqrt{5}}/4\)
16. 16; 81