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Реши любую задачу с помощью нейросети.
$$cos^{2}{left (x right )} – 3 cos{left (x right )} + 2 = 0$$
преобразуем
$$cos^{2}{left (x right )} – 3 cos{left (x right )} + 2 = 0$$
$$cos^{2}{left (x right )} – 3 cos{left (x right )} + 2 = 0$$
Сделаем замену
$$w = cos{left (x right )}$$
Это уравнение вида
a*w^2 + b*w + c = 0
Квадратное уравнение можно решить
с помощью дискриминанта.
Корни квадратного уравнения:
$$w_{1} = frac{sqrt{D} – b}{2 a}$$
$$w_{2} = frac{- sqrt{D} – b}{2 a}$$
где D = b^2 – 4*a*c – это дискриминант.
Т.к.
$$a = 1$$
$$b = -3$$
$$c = 2$$
, то
D = b^2 – 4 * a * c =
(-3)^2 – 4 * (1) * (2) = 1
Т.к. D > 0, то уравнение имеет два корня.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b – sqrt(D)) / (2*a)
или
$$w_{1} = 2$$
$$w_{2} = 1$$
делаем обратную замену
$$cos{left (x right )} = w$$
Дано уравнение
$$cos{left (x right )} = w$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = pi n + {acos}{left (w right )}$$
$$x = pi n + {acos}{left (w right )} – pi$$
Или
$$x = pi n + {acos}{left (w right )}$$
$$x = pi n + {acos}{left (w right )} – pi$$
, где n – любое целое число
подставляем w:
$$x_{1} = pi n + {acos}{left (w_{1} right )}$$
$$x_{1} = pi n + {acos}{left (2 right )}$$
$$x_{1} = pi n + {acos}{left (2 right )}$$
$$x_{2} = pi n + {acos}{left (w_{2} right )}$$
$$x_{2} = pi n + {acos}{left (1 right )}$$
$$x_{2} = pi n$$
$$x_{3} = pi n + {acos}{left (w_{1} right )} – pi$$
$$x_{3} = pi n – pi + {acos}{left (2 right )}$$
$$x_{3} = pi n – pi + {acos}{left (2 right )}$$
$$x_{4} = pi n + {acos}{left (w_{2} right )} – pi$$
$$x_{4} = pi n – pi + {acos}{left (1 right )}$$
$$x_{4} = pi n – pi$$
x2 = 2*pi
x3 = -re(acos(2)) + 2*pi – I*im(acos(2))
x4 = I*im(acos(2)) + re(acos(2))
x1 = 18.8495555497000
x2 = 6.28318403479000
x3 = -12.5663705508000
x4 = -37.6991105864000
x5 = -75.3982245874000
x6 = -56.5486673891000
x7 = 87.9645955876000
x8 = -31.4159267343000
x9 = -87.9645955575000
x10 = -69.1150387764000
x11 = 75.3982235114000
x12 = -56.5486686263000
x13 = 6.28318657126000
x14 = -37.6991118775000
x15 = 81.6814079443000
x16 = 50.2654811803000
x17 = -100.530964660000
x18 = 94.2477808851000
x19 = -69.1150375400000
x20 = 12.5663696339000
x21 = -69.1150378835000
x22 = 18.8495560792000
x23 = -100.530964552000
x24 = -43.9822984008000
x25 = 62.8318527125000
x26 = -18.8495553099000
x27 = 100.530963868000
x28 = -6.28318510897000
x29 = -81.6814102528000
x30 = 75.3982241008000
x31 = 81.6814099713000
x32 = -12.5663702259000
x33 = 18.8495567909000
x34 = 62.8318532824000
x35 = 50.2654837285000
x36 = -37.6991131096000
x37 = -25.1327403746000
x38 = 87.9645930724000
x39 = 100.530964748000
x40 = -81.6814090386000
x41 = 87.9645943362000
x42 = 0.0
x43 = 69.1150390204000
x44 = -43.9822958485000
x45 = -43.9822971745000
x46 = -25.1327416133000
x47 = 56.5486675871000
x48 = -31.4159274784000
x49 = -6.28318638270000
x50 = -50.2654813807000
x51 = 31.4159261903000
x52 = 6.28318528413000
x53 = -87.9645929959000
x54 = 12.5663704265000
x55 = -75.3982238952000
x56 = 81.6814092137000
x57 = -94.2477794313000
x58 = 43.9822959142000
x59 = 62.8318539562000
x60 = 31.4159264886000
x61 = -56.5486676014000
x62 = 31.4159269373000
x63 = 37.6991107807000
x64 = -50.2654822702000
x65 = 56.5486688750000
x66 = 94.2477796094000
x67 = 31.4159257044000
x68 = 69.1150378026000
x69 = 37.6991120523000
x70 = 94.2477783270000
x71 = -62.8318536921000
x72 = 50.2654824463000
x73 = -81.6814077446000
x74 = -75.3982226148000
x75 = -62.8318524749000
x76 = -94.2477785034000
x77 = -18.8495565271000
x78 = -12.5663714609000
x79 = -5215.04380391000
x80 = -1.24358883358000e-6
x81 = 37.6991128568000
x82 = 75.3982228699000
x83 = -6.28318426062000
x84 = -31.4159254513000
x85 = 25.1327418552000
x86 = 43.9822984433000
x87 = 43.9822971695000
x88 = 62.8318531044000
x89 = 12.5663717120000
x90 = -25.1327409216000
x91 = -87.9645943583000
x92 = -50.2654835459000
x93 = 25.1327406378000
x94 = 1.29789534933000e-6
x95 = -94.2477807088000
x96 = 56.5486667492000
