Задача 71777 ...

6182340a3d5d7c0560db11d7

25.05.2023 14:40:01

неравенство решить
sqrt(2) × (e)^(|ln(x/2)|) ≥ sqrt( 9-x)

5f3ea7e3faf909182968ddd9

25.05.2023 15:58:46

★

[m]\left\{\begin {matrix}ln\frac{x}{2}>0\\\sqrt{2}e^{ln\frac{x}{2}} ≥ \sqrt{9-x}\end {matrix}\right.[/m] или [m]\left\{\begin {matrix}ln\frac{x}{2}<0\\\sqrt{2}e^{-ln\frac{x}{2}} ≥ \sqrt{9-x}\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}\frac{x}{2}>1\\\sqrt{2}\frac{x}{2} ≥ \sqrt{9-x}\end {matrix}\right.[/m] или [m]\left\{\begin {matrix}0 <\frac{x}{2}<1\\\sqrt{2}\frac{2}{x} ≥ \sqrt{9-x}\end {matrix}\right.[/m]


[m]\left\{\begin {matrix}x>2\\x ≥ \sqrt{18-2x}\end {matrix}\right.[/m] или [m]\left\{\begin {matrix}0 <x<2\\\frac{2\sqrt{2}}{x} ≥ \sqrt{9-x}\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}x>2\\x ≤9\\ x^2 ≥ 18-2x\end {matrix}\right.[/m] или [m]\left\{\begin {matrix}0 <x<2\\x ≤9\\ \frac{8}{x^2} ≥ 9-x\end {matrix}\right.[/m]

D=76
x_(1)=-1-sqrt(19); x_(2)=-1+sqrt(19)

(2;-1+sqrt(19)] - решение первой системы


[m]\frac{8-9x^2+x^3}{x^2} ≥ 0[/m] ⇒[m]\frac{(x-1)(-9x-8)}{x^2} ≥ 0[/m] ⇒ x ≤ -8/9 или x ≥ 1

[1;2) - решение второй системы

О т в е т. [1;2)U(2;-1+sqrt(19)]