<span>1) cos 3x - cos 5x = sin 4x2sin4xsinx=sin4x sin4x(2sinx-1)=0sin4x=0 x=Пk sinx=1/2 x=(-1)^kП/6+Пn2) cos x + cos 3x = 4 cos 2x2cos2xsinx=4cos2xcos2xsinx-2cos2x=0cos2x(sinx-2)=0cos2x=0x=П/4+Пj/23) cos x cos 2x - sin x sin 2x=сos(x+2x)=cos3x=0 3x=П/2+Пk x=П/6+Пk/34) sin 3x = sin 2x cos xsin(2x+x)=sin2xcosx+sinxcos2xsinxcos2x=0x=Пkx=П/4+Пn/25) cos 3x cos x=1/2(cos4x+cos2x) = cos 2x2cos2x=cos4x+cos2x cos2x=cos4xcos4x-cos2x=0 -2sin3xsinx=0sinx=0 x=пk sin3x=0 x=пk/36) cos x + cos 2x + cos 4x = 0cosx+2cosxcos3x=0cosx(1+2cos3x)=0x=п/2+Пkcos3x=-1/23x=+-(П-П/3)+2Пk3x=+-2П/3+2Пkx=+-2П/9+2Пk/3</span>
1) 5X^2 - 11X + 2 = 0
D = 121 - 40 = 81 ;√ D = 9
X1 = ( 11 + 9 ) : 10 = 2
X2 = ( 11 - 9 ) : 10 = 0,2
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2) 6X^2 - X - 15 = 0
D = 1 + 360 = 361 ; √ D = 19
X1 = ( 1 + 19 ) : 12 = 5/3 = 1 2/3
X2 = ( 1 - 19 ) : 12 = - 18/12 = - 1,5
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3) 7X^2 - X - 6 = X*( X - 6)
7X^2 - X - 6 = X^2 - 6X
7X^2 - X^2 - X + 6X - 6 = 0
6X^2 + 5X - 6 = 0
D = 25 + 144 = 169 ; √ D = 13
X1 = ( - 5 + 13 ) : 12 = 8/12 = 2/3
X2 = ( - 5 - 13 ) : 12 = - 18/12 = - 1,5
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4) 3X*( X^2 - 2X) - X^2 *( X + 1 ) = 2X^3 - 6X - 1
3X^3 - 6X^2 - X^3 - X^2 = 2X^3 - 6X - 1
2X^3 - 7X^2 = 2X^3 - 6X - 1
7X^2 - 6X - 1 = 0
D = 36 + 28 = 64 ; √ D = 8
X1 = ( 6 + 8) : 14 = 1
X2 = ( 6 - 8) : 14 = - 2/14 = - 1/7
Из того что вы записали можно только упростить. Напишите чему это все равно. Тогда можно найти значение х.
8х-20-24+9х=10
17х-44=10
17х=54
х=54/17
х=3 1/18
Arccos(-1/2)=П-arccos(-1/2)=П-П/3=2/3П
t=2/3П=120 градусов
arccos√2/2=П/4
t=П/4=45 градусов.