155
x^5y*(xy^3z)=x^6y^4z
4ab*(-a^2)(-b^3)=4a^3b^4
-1\5p^3q^4*5p^2q^3=-p^5q^7
-11a²b*0,3a²b²=-3,3a^4b³
4\9xy³*2\3xy=8\27x²y^4
-0,6m²n*(-10mn²)=6m³n³
156
xy*(-7xy²)*4x²y=-28x^4y^4
10a²b*(-ab²)*0,6a³=-6a^6b³
0,3m²*(-1\3n^4m^6)=-0,3n^4m^8
a²b*(-ab)*(-ab²)=-a^4b^4
157
(3a²)³=3³a^6=27a^6
(-2x^4y²)³=-8x^12y^6
(-m²nk³)^5=-m^10n^5k^15
(2ab²)²=4a²b^4
<span>Решите уравнение : √2(sinx+cosx)=4sinxcosx
----------------------------------
</span><span> √2(sinx+cosx)=4sinxcosx ; </span>
√2*√2sin(x+π/4)=2sin2x ;
sin2x - sin(x+π/4) =0 ; * * * sinα - sinβ =2sin( (α-β)/2 ) * cos(<span>(α+β)/2) * * *</span>
2sin(x/2 -π/8)*cos(3x/2+π/8) =0⇔(совокупность) [ sin(x/2 -π/8) =0 ;cos(3x/2+<span>π/8) =0 .
</span>a)
sin(x/2 -π/8) =0 ;
x /2-π/8) =π*n ,n∈Z ;
x = π/4+2π*n , n<span><span>∈Z.
</span>--- или ---
b)
</span>cos(3x/2+<span>π/8) =0 ;
</span>3x/2+π/8 = π/2 + π*k , k n<span>∈Z ;
x =</span>π/4+2π*k/ 3 , k <span>∈Z.
</span>
ответ : π/4+2π*k/3 , k ∈Z .
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * cерия <span> решений π/4 +2πn</span> получается из π/4+2πk/3 ,если k =3n . * * *
* * * π/4 +2πn = π/4+2πk/3 ⇒<span>k= 3n * * *
</span>* * * * * *
Удачи !
asinα +bcosα =√(a²+b²)sin(α +β) ,где β =arctq(b/a)
3( Х - 0,8 ) + 2,6 - 6 = - 7х - 4( 0,7 - 2х )
3х - 2,4 - 3,4 = - 7х - 2,8 + 8х
3х - 5,8 = Х - 2,8
2х = 3
Х = 1,5