Задачи на повторение по разным темам. Часть 4

Условия задач

  1. x|2x+1|-3x-4=0
  2. x^2-5x\cdot\frac{|x-2|}{x-2}-14=0
  3. (8x^2-3x+1)^2=32x^2-12x+1
  4. \frac{(x^4-5x^2+4)(x^4+7x^2-18)}{(x-4)^2(3x-5)}\geq 0
  5. \frac{x^2-7|x|+10}{x^2-6x+9}<0
  6. \sqrt{x+7}\cdot\sqrt{3x-2}=3\sqrt{x-1}\cdot\sqrt{x+2}
  7. \sqrt{1+x\sqrt{x^2+42}}=x+1
  8. \sqrt{2x+3}+\sqrt{3x+2}=\sqrt{2x+5}+\sqrt{3x}
  9. \sqrt{4-\sqrt{1-x}}-\sqrt{2-x}>0
  10. \left\{\begin{array}{l l} (x+y+1)^2+(x+y)^2=25,\\ x^2-y^2=3\end{array}\right.
  11. \left\{\begin{array}{l l} \sqrt{\frac{y}{x}}-2\sqrt{\frac{x}{y}}=2,\\ \sqrt{5x+y}+\sqrt{5x-y}=4 \end{array}\right.

Ответ

  1. 2
  2. -7; 7
  3. 0; 3/8; (3\pm\sqrt{73})/16
  4. [-2;-\sqrt{2}]\cup [-1;1]\cup [\sqrt{2};5/3)\cup [2;4)\cup (4;+\infty)
  5. (-5; -2)\cup (2;3)\cup (3;5)
  6. 2
  7. 9,5; 0
  8. 3
  9. (\frac{\sqrt{13}-5}{2}; 1]
  10. (-19/8; -13/8), (2;1)
  11. (1;4)