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kisakamiren
@kisakamiren
July 2022
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Решите уравнение:
16cos^{4}x -24cos^{2} x+9=0[tex]
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Lesben
16cosˇ4 x -24cosˇ2 x +9=0
cosˇ2 x=z
16zˇ2 -24z+9=0
(4z)ˇ2 -2.4z.3 +3ˇ2=0
(4z-3)ˇ2 =0
4z-3=0, 4z=3, z=3/4
cosˇ2 x=3/4
1)cosx=√3/2
x=π/6+2k.π
x=11π/6+2k.π
2)cosx=-√3/2
x=5π/6+2k.π
x=7π/6+2k.π
k∈Z
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Answers & Comments
cosˇ2 x=z
16zˇ2 -24z+9=0
(4z)ˇ2 -2.4z.3 +3ˇ2=0
(4z-3)ˇ2 =0
4z-3=0, 4z=3, z=3/4
cosˇ2 x=3/4
1)cosx=√3/2
x=π/6+2k.π
x=11π/6+2k.π
2)cosx=-√3/2
x=5π/6+2k.π
x=7π/6+2k.π
k∈Z