Предмет: Математика, автор: Tomika13

100БАЛЛОВ ПОМОГИТЕ ПОЖАЛУЙСТАА

!!!С 6-ОГО ЗАДАНИЯ !!!!

Приложения:

Ответы

Автор ответа: LessonAssistant

Ответ:

6. x = 5.

7. x₁ = 1, x₂ = 5.

8. x = 1.

9. x ∉ R.

10. x ∉ ∅.

11. x = 1.

12. x = 4.

Пошаговое объяснение:

6. $\sqrt{x+20} - \sqrt{x - 1} = 3$

$\sqrt{x+20} = 3 + \sqrt{x - 1}$

$x + 20 = 9 + 6\sqrt{x- 1} + x - 1$

$20 = 8 + 6\sqrt{x- 1}$

$-6\sqrt{x- 1} = 8 -20$

$-6\sqrt{x- 1} = -12$

$\sqrt{x- 1} = 2$

x - 1 = 4

x = 5

Проверка:

$\sqrt{5 + 20} - \sqrt{5 - 1} = 3$

3 = 3.

7. $\sqrt{2x - 1} - \sqrt{x - 1} = 1$

$\sqrt{2x - 1} = 1 + \sqrt{x - 1}$

$2x - 1 = 1 + 2\sqrt{x-1} + x - 1$

$-2\sqrt{x-1} = 1 + x - 2x$

$-2\sqrt{x-1} = 1 - x$

$4 (x - 1) = 1 - 2x + x^{2}$

$4(x-1)-(1-x)^2=0$

$4(x-1)-(-(x-1))^2 = 0$

$4(x-1)-(x-1)^2=0$

(x - 1) * (4 - 1 (x - 1)) = 0

(x - 1) * (4 - x + 1) = 0

(x - 1) * (5 - x) = 0

$\left \{ {{x-1 = 0} \atop {5 - x = 0}} \right. \left \{ {x = 1} \atop {x = 5}} \right.$

$\left \{ {{\sqrt{2 * 1 - 1} - \sqrt{1 -1} = 1} \atop {\sqrt{2 * 5 - 1} - \sqrt{5 -1} = 1}} \right.$

$\left \{ {{1 = 1} \atop {1 = 1}} \right.$

$\left \{ {{x = 1} \atop {x=5}} \right.$

x₁ = 1, x₂ = 5

8. $\sqrt {5x + 20} - \sqrt {x + 8} = 2$

$\sqrt {5x + 20} = 2 + \sqrt {x + 8}$

$5x + 20 = 4 + 4\sqrt {x+8} + x + 8$

$-4\sqrt {x+8} = 12 + x - 5x - 20$

$-4\sqrt {x+8} = -8 - 4x$

$\sqrt {x+8} = 2 + x$

$x + 8 = 4 + 4x + x^2$

$x + 8 -4 -4x-x^2 = 0$

$-3x+4-x^2=0$

$-x^2-3x+4=0$

$x^2+3x -4 = 0$

D = b² - 4ac = 9 + 16 = 25 ( $\sqrt{25}=5$ )

x₁ = $\frac{-b + \sqrt{D}}{2a} = \frac{-3+5}{2} = 1$

x₂ = $\frac{-b - \sqrt{D}}{2a} = \frac{-3-5}{2} = -4$

$\left \{ {{\sqrt{5*1 + 20} - \sqrt{1+8}=2} \atop {{\sqrt{5*(-4) + 20} - \sqrt{-4+8}=2}}} \right. \left \{ {{\sqrt{2=2}} \atop {-2=2}} \right. \left \{ {{x=1} \atop {x\neq -4}} \right.$

x = 1.

9. $3\sqrt{4-x}+\sqrt{5+x}=30$

$3\sqrt{4-x}= 30 -\sqrt{5+x}$

$9(4-x)=900-60\sqrt{5+x} + 5 +x$

$36-9x=905-60\sqrt{5+x}+x$

$60\sqrt{5+x}=905+x-36+9x$

$60\sqrt{5+x}=869+10x$

$3600(5+x)=869^2+17380x+100x^2$

$18000+3600x=869^2+17380x-100x^2$

$18000+3600x - 869^2-17380x-100x^2=0$

$18000-13780x-869^2-100x^2=0$

$-100x^2-13780x+18000-869^2=0$

$100x^2 + 13780x - 18000+869^2=0$

$x = \frac{-13780 +- \sqrt{13780^2-4*100(-18000+869^2}}{2*100}$

$x = \frac{-13780 +- \sqrt{13780^2-400(-18000+869^2}}{200}$

x ∈ R

10. $\sqrt{1-x} + \sqrt{1+x} = 1$

$1-x+2\sqrt{(1-x)*(1+x)} + 1 + x = 1$

$2\sqrt{1-x^2} + 1 - 0$

x ∈ ∅

11. $\sqrt{x+1} + \sqrt{x-1}=\sqrt{3x-1}$

$x+1+2\sqrt{(x+1)*(x-1)} + x -1 = 3x-1$

$x+1+2\sqrt{x^2-1} +x = 3x$

$2x + 1 + 2\sqrt{x^2-1} - 3x$

$2\sqrt{x^2-1} = 3x - 2x - 1$

$2\sqrt{x^2-1} = x - 1$

$4(x^2-1)=x^2-2x+1$

$4x^2-4=x^2-2x+1$

$4x^2-4-x^2+2x-1=0$

$3x^2-5+2x=0$

$3x^2+2x-5=0$

D = b² - 4ac = 4 + 60 = 64 ( $\sqrt{64}=8$ )

x₁ = $\frac{-b+\sqrt{D} }{2a} = \frac{-2+8}{6} = 1 [/tex}</p><p>x₂ = [tex]\frac{-b-\sqrt{D} }{2a} = \frac{-2-8}{6} = \frac{5}{3} [/tex}</p><p>[tex]\left \{ {\sqrt{1+1}+\sqrt{1-1}=\sqrt{3*1-1}} \atop {\sqrt{-\frac{5}{3}+1}}}+\sqrt{-\frac{5}{3} - 1} = \sqrt{3*(-\frac{5}{3}) -1} \right. \left \{ {{1,41421=1,41421} \atop {\sqrt{-\frac{2}{3}}}+\sqrt{-\frac{5}{3} - 1} = \sqrt{3*(-\frac{5}{3}) -1}} \right. \left \{ {{x=1} \atop {x\neq -\frac{5}{3}}} \right.$