2-2cos²x+4+3√3cosx=0 cosx=a 2a²-3√3a-6=0 D=27+48=75 a1=(3√3-5√3)/4=-√3/2⇒cosx=-√3/2⇒x=+-5π/6+2πn,n∈z a2=(3√3+5√3)/4=2√3⇒cosx=2√3>1 нет решения -5π/2≤-5π/6+2πn≤-π -15≤-5+12n≤-6 -10≤12n≤-1 -5/6≤n≤-1/6 нет решения -5π/2≤5π/6+2πn≤-π -15≤5+12n≤-6 -20≤12n≤-11 -5/3≤n≤-11/12 n=-1⇒x=5π/6-2π=-7π/6∈[-5π/2;-π]
Answers & Comments
Verified answer
2-2cos²x+4+3√3cosx=0cosx=a
2a²-3√3a-6=0
D=27+48=75
a1=(3√3-5√3)/4=-√3/2⇒cosx=-√3/2⇒x=+-5π/6+2πn,n∈z
a2=(3√3+5√3)/4=2√3⇒cosx=2√3>1 нет решения
-5π/2≤-5π/6+2πn≤-π
-15≤-5+12n≤-6
-10≤12n≤-1
-5/6≤n≤-1/6
нет решения
-5π/2≤5π/6+2πn≤-π
-15≤5+12n≤-6
-20≤12n≤-11
-5/3≤n≤-11/12
n=-1⇒x=5π/6-2π=-7π/6∈[-5π/2;-π]