Question

Прошу решите срочно нужно

Answer 1

1)
$log_ frac{1}{3} (x-1) geq -2 \ left { {{x-1 leq 9} atop {x-1 textgreater 0}} right. \ left { {{xleq10} atop {x textgreater 1}} right.$
x ∈ (1; 10]

2)
$13^{2x+1} -13^x-12=0 \ 13^x=t \ 13t^2-t-12=0 \ D=1+13*48=625 \ x_1=- frac{12}{13} \ x_2=1 \ \ 13^x=- frac{12}{13} \ 13^x=1$

x ∈ ∅
x = 0

x = 0

3) cos α = 0,8;  0 < α < π/2
$left { {{|sin alpha|= sqrt{1-0,8^2} } atop {0 textless alpha textless frac{ pi }{2} }} right.$
sin α = 0,6
tg α = sin α / cos α = 0,6/0,8 = 3/4
ctg α = 1 / tg α = 4/3

4)
$sqrt{x-1}=x-3 \ left { {{x-1=x^2-6x+9} atop {x-3 geq 0}} right.\ left { {{x^2-7x+10=0} atop {x geq 3}} right.\ left { {{x_1=2;x_2=5} atop {x geq 3}} right. \ x=5$

5)
$sqrt{2+x-x^2} textgreater -1$
2 + x - x² ≥ 0
x² - x - 2 ≤ 0
x² - x - 2 = 0
По теореме Виета:
x₁ = -1, x₂ = 2
x ∈ [-1; 2]