[tex] \sqrt{9x-8-x^2} (cos2x+3 \sqrt{3}sinx-4)=0 [/tex]
x²-9x+8≤0
x1+x2=9 U x1*x2=8⇒x1=1 U x2=8
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x∈[1;8]
cos2x+3√3sinx-4=0
1-2sin²x+3√3sinx-4=0
2sin²x-3√3sinx+3=0
sinx=a
2a²-3√3a+3=0
D=27-24=3
a1=(3√3-√3)/4=√3/2⇒sinx=√3/2⇒x=(-1)^n *π/3_πn
a2=(3√3+√3)/4=√3⇒sinx=√3∉[-1;1]
Ответ х=1 х=8 х=π/3 х=2π/3 х=5π/3 х=8π/3
