1)
a³ + b³ = (a+b)(a² -ab+b²)
a=2x+y
b=x-2y
(2x+y)³ + (x-2y)³=(2x+y+x-2y)((2x+y)² -(2x+y)(x-2y)+(x-2y)²)=
=(3x-y)(4x²+4xy+y² -(2x³+xy-4xy-2y²)+x² -4xy+4y²)=
=(3x-y)(4x² +4xy+y² -2x³ +3xy +2y² +x² -4xy+4y²)=
=(3x-y)(5x² -2x³ +7y² +3xy)=15x³-5x²y-6x⁴+2x³y+21xy²-7y³+9x²y-3xy²=
=15x³ -6x⁴ -7y³ +2x³y+4x²y+18xy²
2)
(2mn-1)³ +1³ =(2mn-1+1)((2mn-1)² -(2mn-1)*1+1²)=
=2mn(4m²n²-4mn+1-2mn+1+1)=2mn(4m²n²-6mn+3)=8m³n³-12m²n²+6mn
3)
a²+4b² -9c² -4ab=(a² -4ab+4b²)-9c² =(a-2b)² -9c² =(a-2b-3c)(a-2b+3c)
4)
x³ +x² -xy² -y² =(x³ +x²)-(xy² +y²)=x²(x+1)-y²(x+1)=(x+1)(x² -y²)=
=(x+1)(x-y)(x+y)
У=ln х-1/х+1y'=1/x+1/(x+1)^2=(x^2+3x+1)/x(x+1)y'=1/x+1/x^2=x^2+x=(1+x)/x^2<span>y'=(2*sqrt(x^2+1)-2x(2x)*(1/2)/sqrt(x^2+1))/(x^2+1)=sqrt(x^2+1)/(x^2+1)^2</span>
3х'2-2Х-1 <0
3x'2-2X-1=0
D=4+12
D=16
x1,2=2+/-4/6
x1=1
x2=-1/3
Будет равно : 0,6an^39 n^91