<span>Sin(π+3x/4)-sin(3π/2-3x/4)=0</span>
-sin(3x/4)-cos(3x/4)=0
sin(3x/4)+cos(3x/4)=0
sin(3x/4+π/4)=0
sin(3x/4+π/4)=0
3x/4+π/4=πn, n∈Z
3x/4=πn-π/4, n∈Z
<u>x=(4πn-π)/3, n∈Z</u>
{x-5y=3
{xy+3y=11
х=(3+5у)
(3+5у)×у+3у=11
3у+5у²+3у-11=0
5у²+6у-11=0
D=(-6)²-4×5×(-11)=36+220=256
y1=(-6-√256)/2×5=(-6-16)/10=(-22/10)=-2,2
y2=(-6+√256)/2×5=(-6+16)/10=10/10=1
x1=(3+5y1)
x1=(3+5×(-2,2))
x1=3-11
x1=-8
x2=(3+5y2)
x2=(3+5×1)
x2=3+5
x2=8
(-8;-2,2); (8;1).
P=20 см, S=24 <span>см²</span>
P=2*(a+b)
20=2*(a+b)
10=a+b
a=10-b
S=a*b
24=a*b - <span>подставим значение а из периметра и получим
24=(10-b)*b
</span>
![24=10b- b^{2}](https://tex.z-dn.net/?f=24%3D10b-+b%5E%7B2%7D+)
![-b^{2}+10b-24=0](https://tex.z-dn.net/?f=-b%5E%7B2%7D%2B10b-24%3D0)
![D= b^{2}-4ac= 10^{2}-4*(-1)*(-24)=100-96=4](https://tex.z-dn.net/?f=D%3D+b%5E%7B2%7D-4ac%3D+10%5E%7B2%7D-4%2A%28-1%29%2A%28-24%29%3D100-96%3D4)
![b_{1}=\frac{-b+\sqrt{D}}{2a}=\frac{-10+\sqrt{4}}{-2}=\frac{-10+{2}}{-2}=4](https://tex.z-dn.net/?f=+b_%7B1%7D%3D%5Cfrac%7B-b%2B%5Csqrt%7BD%7D%7D%7B2a%7D%3D%5Cfrac%7B-10%2B%5Csqrt%7B4%7D%7D%7B-2%7D%3D%5Cfrac%7B-10%2B%7B2%7D%7D%7B-2%7D%3D4)
![b_{2}=\frac{-b-\sqrt{D}}{2a}=\frac{-10-\sqrt{4}}{-2}=\frac{-10-{2}}{-2}=6](https://tex.z-dn.net/?f=b_%7B2%7D%3D%5Cfrac%7B-b-%5Csqrt%7BD%7D%7D%7B2a%7D%3D%5Cfrac%7B-10-%5Csqrt%7B4%7D%7D%7B-2%7D%3D%5Cfrac%7B-10-%7B2%7D%7D%7B-2%7D%3D6)
сторона a=4 см, сторона b=6 см
Проверка:
P=2*(a+b)=2*(4+6)=20 см
S=a*b=4*6=24 см²