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MorevaAlyona1408
@MorevaAlyona1408
August 2022
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3sin в квадратех-5sinx-2=0
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13iul
3 sin²x - 5sinx - 2 = 0
Пусть sin x = y, тогда
3 y² - 5y - 2 = 0
D = (-5)² - 4*3*(-2) = 25+24 = 49
y₁= (5 - √49) / (2 * 3)= - 2/6 = - 1/3
y₂ = (5 +
√49
)/(2*3) = 12/6 = 2
sin x = 2 - не имеет корней
sin x = -1/3
x = (-1)ⁿ arcsin(-1/3) + πk, k∈Z
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Answers & Comments
Пусть sin x = y, тогда
3 y² - 5y - 2 = 0
D = (-5)² - 4*3*(-2) = 25+24 = 49
y₁= (5 - √49) / (2 * 3)= - 2/6 = - 1/3
y₂ = (5 + √49)/(2*3) = 12/6 = 2
sin x = 2 - не имеет корней
sin x = -1/3
x = (-1)ⁿ arcsin(-1/3) + πk, k∈Z