<span> (х+1)+(х+2)+(х+3)+...+(х+28)=155
всего членов 28
28х+1+2+3+....+27+28=155
Sn=(1+28)/2*28=29*14=406
28x+406=155
28x=155-406
28x=-251
x=-251/28=-8 27/28
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</span><span>(х+1)+(х+4)+(х+7)+...+(х+28)=155
</span>10 чденов
10x+1+4+....+28=155
Sn=(1+28)/2*10=29*5=145
10x=10
x=1
1+sinx·cosx-3cos²x=0
sin^2x+cos^2x+sinxcosx-3cos^2x=0/cos^2x
tg^x+1+tgx-3=0
a^2+a-2=0
D=3
a1=-2
a2=-1 x=-pi/4+pin
3) sinxcosx-cos^2x=1
tgx-1=1
tgx=2
x=arctg2+pin
3х - 5у = - 18
- 2х + 7у = 36
Решение
2х = 7у - 36
Х = 3,5у - 18
3( 3,5у - 18 ) - 5у = - 18
10,5у - 54 - 5у = - 18
5,5у = - 18 + 54
у = 36 : 5,5
у = 36 : ( 11/2 ) = 72/11 = 6 6/11
Х = 7/2 • 72/11 - 18 = ( 252/11 ) - 18 = 22 10/11 - 18 = 4 10/11
Ответ ( 4 10/11 ; 6 6/11 )
cos x = cos 5x
cos 5x=cos 4x cos x - sin 4x sin x
cos x = cos 4x cos x - sin 4x sin x
cos 4x = cos^2 x
sin 4x =4 sin x cos x
cos x = cos^2 x cos x - 4 sin x cos x
cos x = cos 5x
cos 5x - cos x = 0
cos 5x - cos x = - 2 sin ((5x + x)/2) sin ((5x - x)/2) = -2 sin 3x sin 2x = 0
a) sin 3x = 0 тривиально
b) sin 2x = 0 тривиально
(4x - 3y)^2 - (2x + y)(3x - 5y)
(16x^2 - 24xy + 9y^2) - (6x^2 - 10xy + 3xy - 5y^2)
16x^2 - 24xy +9y^2 - 6x^2 + 10xy - 3xy + 5y^2
10x^2 + 14y^2 - 17xy
10x^2 - 17xy + 14y^2
<u>Ответ: 10x^2 - 17xy + 14y^2</u>