Урок 10. Уравнения и неравенства с радикалами.

Домашнее задание из В.В. Ткачук “Математика – абитуриенту”

1. $$(x^2-4)\sqrt{x+1}=0$$
2. $$\sqrt{2x-6}+\sqrt{x+4}=5$$
3. $$\sqrt{2x+5}-\sqrt{3x-5}=2$$
4. [2] $$\sqrt{x+1}-1=\sqrt{x-\sqrt{x+8}}$$
5. $$\sqrt{2x^2+8x+7}-x=2$$
6. $$x+\sqrt{2x^2-7x+5}=1$$
7. [2] $$\sqrt{x+2}-\sqrt{x-1}=\sqrt{2x-3}$$
8. $$\sqrt{x^2-3x+2}-3-x>0$$
9. $$x+4\leq \sqrt{x+46}$$
10. $$x-3<\sqrt{x+27}$$
11. $$\sqrt{x^2+2x-3}<x$$
12. $$\sqrt{x^2-x-2}\leq x-1$$
13. $$x+4<\sqrt{-x^2-8x-12}$$
14. $$\frac{3-x}{\sqrt{15-x}}<1$$
15. $$\frac{\sqrt{x+5}}{1-x}<1$$
16. $$\frac{\sqrt{24-2x-x^2}}{x}<1$$
17. $$\sqrt{1-3x}-\sqrt{5+x}>1$$
18. [2] $$\frac{\sqrt{6+x-x^2}}{2x+5}\geq \frac{\sqrt{6+x-x^2}}{x+4}$$
19. $$(x+1)\sqrt{x^2+x-2}=2x+2$$
20. $$x\sqrt{36x+1261}=18x^2-17x$$
21. $$\sqrt{(x-4)(5x+41)}<2(2x-7)$$
22. $$\frac{\sqrt{51-2x-x^2}}{1-x}<1$$
23. $$\sqrt{x}\leq x-1$$
24. $$(x+2)\sqrt{x^2+7x+6}\geq 0$$
25. $$\sqrt{2x^2+x}>1+2x$$
26. $$\sqrt{4-6x-x^2}=x+4$$
27. $$(x^2-18x+77)\sqrt{10-x}\geq 0$$
28. $$\frac{\sqrt{x^2+x-6}+3x+13}{x+5}>1$$
29. $$x+\sqrt{x^2+x-6}>-1$$
30. $$2x-7<\sqrt{81-x^2}$$

Ответы к домашнему заданию урока 10 из В.В. Ткачук “Математика – абитуриенту”

1. -1; 2
2. 5
3. 2
4. 8
5. -1
6. 1
7. 2
8. $$(-\infty; -7/9)$$
9. [-46; 3]
10. [-27; 9)
11. [1; 3/2)
12. [2; 3]
13. $$[-6; -4+\sqrt{2})$$
14. (-1; 15)
15. $$[-5; -1)\cup (1; +\infty)$$
16. [-6; 0)U(3; 4]
17. $$[-5; -(9-\sqrt{61})/8)$$
18. 3; [-2; -1]
19. -3; 2
20. 0; 3
21. $$[4; 45/11)\cup (8; +\infty)$$
22. $$[-1-2\sqrt{13}; -5)\cup (1; -1+2\sqrt{13}]$$
23. $$[(3+\sqrt{5})/2; +\infty)$$
24. $$-6; [-1; +\infty)$$
25. $$(-\infty; -1/2)$$
26. -1
27. $$(-\infty; 7]; 10$$
28. $$(-\infty; -7)\cup (-5;3]\cup [2; +\infty)$$
29. $$(-\infty; -7)\cup [2; +\infty)$$
30. $$[-9; (34+2\sqrt{29})/5)$$