1) по теореме косинусов имеем: a² = b² + c² - 2bc cos a = 25 - 24 cos 135° = 25 + 12√2 a = √(25 + 12√2) по теореме синусов, a / sin a = b / sin b sin b = sin a · b / a = √2 / 2 · 3 / √(25 + 12√2) = 3 / √(50 + 24√2) ∠b = arcsin(3 / √(50 + 24√2)) ∠c = 180° - 135° - ∠b = 45° - arcsin(3 / √(50 + 24√2)) 2) ∠a = 180° - ∠b - ∠c = 65° по теореме синусов b / sin b = a / sin a b = a sin b / sin a = 24.6 · √2 / 2 / (sin 65°) = 123√2 / (10 sin 65°) по теореме синусов c / sin c = a / sin a c = a sin c / sin a = 24.6 ·sin 70° / sin 65°
x+y+z=4
2xy-z^2=16
z=4-(x+y)
2xy-16+8(x+y)-(x+y)^2=16
2xy-16+8(x+y)-x^2-2xy-y^2=16
-x^2-y^2+8(x+y)=32
(-x^2+8x-16)+(-y^2+8y-16)=0
-(x-4)^2-(y-4)^2=0
-(x-4)^2=(y-4)^2
x-4=0
y-4=0
x=4
y=4
z=-4
x+y+2z=0