1,2X+3,7-0,7=1,3X
1,2X-1,3X=-3,7+0,7
-0,1X=-3|:(-0,1)
X=30
Так решаем через дискриминат:
2y^2-50y=75-3y
2y^2-50y-75+3y=0
2y^2-47y-75=0
D=b^2-4c=2209-(-600)=2809
x1,2=-b±√D/2a=47±53/4=25;-6/4=-3/2
x1=-3/2 x2=25
1) x = 5
2) x = 1/3
3) x = 125
4) x = 8
5) x принадлежит промежутку (2; +бесконечности)
6) x принадлежит промежутку (0; 1)
1) sin a = √2/2; a1 = pi/4+2pi*k; cos a1 = √2/2
a2 = 3pi/4+2pi*k; cos a2 = -√2/2
cos(60 + a1) = cos 60*cos a1 - sin 60*sin a1 =
= 1/2*√2/2 - √3/2*√2/2 = √2/4*(1 - √3) = -√2(√3 - 1)/4
cos(60 + a2) = cos 60*cos a2 - sin 60*sin a2 =
= -1/2*√2/2 - √3/2*√2/2 = -√2/4*(1 + √3) = -√2(√3 + 1)/4
2) sin a = 2/3; cos b = -3/4; a ∈ (pi/2; pi); b ∈ (pi; 3pi/2)
cos a < 0; sin^2 a = 4/9; cos^2 a = 1-4/9 = 5/9; cos a = -√5/3
sin b < 0; cos^2 b = 9/16; sin^2 b = 1-9/16 = 7/16; sin b = -√7/4
sin(a+b) = sin a*cos b + cos a*sin b =
= 2/3*(-3/4) + (-√5/3)(-√7/4) = -6/12 + √35/12 = (√35 - 6)/12
cos(-b) = cos b = -3/4