ОДЗ
x ≠ 2;
x ≠ - 2
x (x - 2) + (x + 2)^2 = 8
x^2 - 2x + x^2 + 4x + 4 = 8
2x^2 + 2x + 4 = 8
2x^2 + 2x - 4 = 0 /:2
x^2 + x - 2 = 0
D = 1 + 8 = 9
x1 = ( - 1 + 3)/2 = 1
x2 = ( - 1 - 3)/2 = - 2 не удовлетворяет ОДЗ
Ответ
x = 1
9 : 8 = x : 2,4
8x = 9 • 2,4
x = 21,6 : 8
x = 2,7
2x-5>0⇒2x>5⇒x>2,5
2x-5<4⇒2x<9⇒x<4,5
x∈(2,5;4,5)
(sinx+sin4x)+(sin2x+sin3x)=0
2sin(5x/2)cos(3x/2)+2sin(5x/2)cos(x/2)=0
2cos(x/2)*(sin(5x/2)+sin(3x/2))=0
4cos(x/2)*sin(2x)cos(x/2)=0
4cos²(x/2)*sin(2x)=0
cos(x/2)=0
x/2=π/2+πk
x=π+2πk,k∈z
sin2x=0⇒2x=πk⇒x=πk/2,k∈z