1.
а)х+7у=2 х+7у=2 8-у+7у=2 6у=-6 у=-1 х=9
х+у=8 х=8-у х=8-у х=8-у х=8+1 у=-1
б)2х+у=11 у=11-2х у=11-2х у=11-2*14 х=14
3х-у=4 3х-11-2х=4 х=14 х=14 у=-17
3.
а)3х-8у=6 * 6х-у=27 6х+27-6х=27 0х=0
3х+7у=21 у=-27-6х у=-27-6х у=-27
* 3х-8у+3х+7у=6+21
6х - у = 27
б)4х+5у=1 * 4х+5у=1 4х+5у=1
5х+7у=5 9х+12у=6 | : 3 ---> 3х+4у=2
* 4х+5у+5х+7у=1+5
9х+12у=6
1. y=x2+x−25D(y):x2+x−2=0(x+2)(x−1)=0x=−2; x=1;D(y)=(−∞;−2)∪(−2;1)∪(1;+∞)
\begin{gathered}2)~\boldsymbol{y=\dfrac5{x^2+x}-2}D(y):x^2+x\neq 0\\x(x+1)\neq 0\\x\neq 0;~~~x\neq -1;boldsymbol{D(y)=(-\infty;-1)\cup(-1;0)\cup(0;+\infty)}\end{gathered}2) y=x2+x5−2D(y):x2+x=0x(x+1)=0x=0; x=−1;D(y)=(−∞;−1)∪(−1;0)∪(0;+∞)
\begin{gathered}3)~\boldsymbol{y=\dfrac5{x^2}+x-2}D(y):x^2\neq 0;~~~x\neq 0;boldsymbol{D(y)=(-\infty;0)\cup(0;+\infty)}\end{gathered}3) y=x25+x−2D(y):x2=0; x=0;D(y)=(−∞;0)∪(0;+∞)
(1-cos2x)/2+(1-cos6x)/2=1
1-cos2x+1-cos6x=2
cos2x+cos6x=0
2cos4ccos2x=0
cos4x=0⇒4x=π/2+πn,n∈z⇒x=π/8+πn/4,n∈z
cos2x=0⇒2x=π/2+πk,k∈z⇒x=π/4+πk/2,k∈z
2
sin3x-sin(π/2-2x)=0
2sin(5x/2-π/4)cos(x/2+π/4)=0
sin(5x/2-π/4)=0⇒5x/2-π/4=πn,n∈z⇒5x/2=π/4+πn,n∈z⇒
x=π/10+2πn/5,n∈z
cos(x/2+π/4)=0⇒x/2+π/4=π/2+πk,k∈x⇒x/2=π/4+πk,k∈z⇒
x=π/2+2πk,k∈z
3
cosx+cos2x=0
2xos3x/2cosx/2=0
cos3x/2=0⇒3x/2=π/2+πn,n∈z⇒x=π/3+2πn/3,n∈z
cosx/2=0⇒x/2=π/2+πk,k∈z⇒x=π|2πk,k∈z