Question

Решить уравнение sqrt(20) sin5x+sqrt(5)=0

 

Answer 1

√20*sin5x + √5 = 0

 

√20*sin5x = -  √5

 

sin5x = -  √(5/20)

 

sin5x = - 1/2

 

5x = - pi/6 +2pik

x= - pi/30 + (2pik)/5, k∈Z

 

5x= 7pi/6 +2pik

x = 7pi/30 + (2pik)/5, k∈Z

 

ОТВЕТ:

- pi/30 + (2pik)/5, k∈Z

7pi/30 + (2pik)/5, k∈Z

 

Answer 2

$sqrt{20}sin(5x)+sqrt{5}=0$

$sin (5x)=-frac{sqrt{5}}{sqrt{20}};$

$sin(5x)=-sqrt{frac{5}{20}}=-sqrt{frac{1}{4}}=-frac{1}{2}$

$5x=(-1)^k*arcsin(-frac{1}{2})+pi*k;$

$5x=(-1)^k*(-frac{pi}{6})+pi*k;$

$x=frac{pi*(-1)^{k+1}}{30}+frac{pi*k}{5}$

 

k є Z