4х-4у-х²+у²=4(х-у)-(х²-у²)=4(х-у)-(х-у)(х+у)=(х-у)(4-х-у)
Y`=(4x-26)*e^(x-17)+(2x²-26x+26)*e^(x-17)=e^(x-17)*(4x-26+2x²-26x+26)=
=e^(x-17)*(2x²-22x)=0
e^(x-17)>0 при любом х
2x(x-11)=0
x=0 x=11
+ _ +
-----------------(0)---------------(11)----------------------
min
ymin=y(11)=(242-286+26)*e^-6=0
0,2x2+0,6x=2,5x-0,5x3
0,5x3+0,2x2-1,9x=0
x(0,5x2+0,2x-1,9)=0
x(5x2+2x-19)=0
D=4+380=384
x=0; (-1+√96)/5; (-1-√96)/5
1) sin a = √2/2; a1 = pi/4+2pi*k; cos a1 = √2/2
a2 = 3pi/4+2pi*k; cos a2 = -√2/2
cos(60 + a1) = cos 60*cos a1 - sin 60*sin a1 =
= 1/2*√2/2 - √3/2*√2/2 = √2/4*(1 - √3) = -√2(√3 - 1)/4
cos(60 + a2) = cos 60*cos a2 - sin 60*sin a2 =
= -1/2*√2/2 - √3/2*√2/2 = -√2/4*(1 + √3) = -√2(√3 + 1)/4
2) sin a = 2/3; cos b = -3/4; a ∈ (pi/2; pi); b ∈ (pi; 3pi/2)
cos a < 0; sin^2 a = 4/9; cos^2 a = 1-4/9 = 5/9; cos a = -√5/3
sin b < 0; cos^2 b = 9/16; sin^2 b = 1-9/16 = 7/16; sin b = -√7/4
sin(a+b) = sin a*cos b + cos a*sin b =
= 2/3*(-3/4) + (-√5/3)(-√7/4) = -6/12 + √35/12 = (√35 - 6)/12
cos(-b) = cos b = -3/4
(1+cos6x)/2=cos6x
1+cos6x=2cos6x
cos6x=1
6x=2πn,n∈Z
x=πn/3,n∈Z