<span>4sinx^2+4sin2x+3cosx^2=0
4Sin</span>²x + 8SinxCosx + 3Cos²x = 0 | : Cos²x≠0
4tg²x +8tgx +3 = 0
решаем как квадратное
D = 16
a) tgx = -1/2 б) tgx = -1,5
x = arctg(-0,5) + πk , k ∈Z x = arctg(-1,5) + πn , n ∈Z
2x+5y=-7
3x- y=15
----------------
2x+5y=-7
15x-5y=75
----------------
17x=68
x=4, y=-3
----------------------------------------------------
x-2y=2
3x-y²=11
-------------
-3x+6y=-6
3x-y²=11
---------------
y²-6y+5=0
y1=1, y2=5
x1=4, x2=12
---------------------------------------------------
x+y=2
xy=-15
-----------
x1=-3, x2=5
y1=5 y2=-3
------------------------------------------------------------
3x-2y=5
2x+5y=16
------------------
6x-4y=10
-6x-15y=-48
-------------------
19y=38
y=2
x=3
Первое:
![x(a+3)-y(a+3)=(a+3)(x-y)](https://tex.z-dn.net/?f=x%28a%2B3%29-y%28a%2B3%29%3D%28a%2B3%29%28x-y%29)
Второе:
![4(x+y)(x-y)+(x+y)^{2}=(x+y)(4x-4y+x+y)=\\=(x+y)(5x-3y)](https://tex.z-dn.net/?f=4%28x%2By%29%28x-y%29%2B%28x%2By%29%5E%7B2%7D%3D%28x%2By%29%284x-4y%2Bx%2By%29%3D%5C%5C%3D%28x%2By%29%285x-3y%29)
Третье:
![2(a-b)^{2}-(a+b)(a-b)=(a-b)(2a-2b-a-b)=(a-b)(a-3b)](https://tex.z-dn.net/?f=2%28a-b%29%5E%7B2%7D-%28a%2Bb%29%28a-b%29%3D%28a-b%29%282a-2b-a-b%29%3D%28a-b%29%28a-3b%29)
Четвёртое:
![(a+b)^{3}-a(a+b)^{2}=(a+b)^{2}(a+b-a)=b(a+b)^{2}](https://tex.z-dn.net/?f=%28a%2Bb%29%5E%7B3%7D-a%28a%2Bb%29%5E%7B2%7D%3D%28a%2Bb%29%5E%7B2%7D%28a%2Bb-a%29%3Db%28a%2Bb%29%5E%7B2%7D)
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(х^2+x^3)/x+1=x^2(1+x)/1+x. 1+x сокращаются и остается y=x^2.