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polinaaa01
@polinaaa01
August 2022
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Решите уравнение: sin 3π/(x+1)=1/2.
В ответе запишите Наибольший положительный корень
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армения20171
Sin3π/(x+1)=1/2
3π/(x+1)=π/6+2πk;k€z
x+1=3π/(π/6+2πk)
x=1-3π/(π/6+2πk)>0
(π/6+2πk-3π)/(π/6+2πk)>0
{π/6+2πk-3π>0
{π/6+2πk>0;k>-π/6:(2π);k>-1/12
2πk>3π-π/6
2πk>17π/6
2k>17/12
k=(2;3;4;......)
k=2
x=1-3π/(π/6+4π)=1-3π*6/25π=
1-18/25=(25-18)/25=7/25
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Answers & Comments
3π/(x+1)=π/6+2πk;k€z
x+1=3π/(π/6+2πk)
x=1-3π/(π/6+2πk)>0
(π/6+2πk-3π)/(π/6+2πk)>0
{π/6+2πk-3π>0
{π/6+2πk>0;k>-π/6:(2π);k>-1/12
2πk>3π-π/6
2πk>17π/6
2k>17/12
k=(2;3;4;......)
k=2
x=1-3π/(π/6+4π)=1-3π*6/25π=
1-18/25=(25-18)/25=7/25