Розв’язати рівняння: 2sin(+х)=

Решите уравнение  : 2sin(√π /3 +x )= √3

* * * * * * * * * * * * * * * * * * * * *

x =   - √π /3 + (-1)ⁿ (π /3) + πn , n ∈  ℤ

Пошаговое объяснение:

* * *   sinx =a ,   |a| ≤ 1  ⇒  x =(-1)ⁿarcsin(a) + πn , n ∈  ℤ .   * * *

2sin(√π /3 +x ) = √3  ⇔ sin(√π /3 +x ) = √3 /2 ⇒

√π /3 + x  = (-1)ⁿ (π /3) + πn , n ∈  ℤ .

1)

{x^2+2y^2=18,x^2-2y^2=14   < => {x^2+2y^2=18,2x^2=32   < => {x^2+2y^2=18,x^2=16 < => {x^2+2y^2=18,x=4 < => {16+2y^2=18,x=4 < => {2y^2=2,x=4 < => {y^2=2/2,x=4 < => {y=1,x=4

2)

{y=x^2+4,x^2+y^2=49 < => {x^2=y-4,y-4+y^2=49 < => {x^2=y-4,y^2+y-4-49=0 < => {x^2=y-4,[y^2+y-53=0,d=1-4*1*(-53)=213,y1=-1-sqrt213/2,y2=-1+sqrt213/2 < => {x^2=-1+sqrt213/2-4,y=-1+sqrt213/2 < => {x=sqrt[-1+sqrt213/2-4],y=-1+sqrt213/2