По условию получаем систему уравнений (если х×у=-75), то:
1-е число-х
2-е число-у
{х+у=20
{х×у=-75
х=(20-у)
(20-у)×у=-75
-у²+20у=-75
у²-20у-75=0
D=(-(-20))²-4×1×(-75)=400+300=700
у1=(-(-20)-√700)/2×1=(20-√700)/2=(20-26,46)/2=-6,46/2=-3,23
у2=(-(-20)+√700)/2×1=(20+26,46)/2=46,46/2=23,23
х1=20-y1
x1=20-(-3,23)
x1=23,23
x2=20-y2
x2=20-23,23
x2=-3,23
проверка: х1×у1=-75
23,23×(-3,23)=-75
-75,0329≈-75
ответ: (23,23;-3,23) и (-3,23;23,23)
если (х×у=75), то
{х+у=20
{х×у=75
х=(20-у)
(20-у)×у=75
20у-у²=75
у²-20у+75=0
D=(-(-20))²-4×1×75=400-300=100
y1=(-(-20)-√100)/2×1=(20-10)/2=10/2=5
y2=(-(-20)+√100)/2×1=(20+10)/2=15
x1=20-y1
x1=20-5
x1=15
x2=20-y2
x2=20-15
x2=5
ответ: (15;5) и (5;15).
sin^4(a) + 2sin^2(a) * cos^2(a) + cos^4(a) = (sin^2(a) + cos^2(a))^2 = 1^2 = 1
2)
(sin(a) + cos(a))^2 + (sin(a) - cos(a))^2 = sin^2(a) + 2sin(a)*cos(a) + cos^2(a) + sin^2(a) - 2sin(a)*cos(a) + cos^2(a) = 1 + 1 = 2
3)
cos^2(a) - cos^4(a) + sin^4(a) = cos^2(a) * (1 - cos^2(a)) + sin^2(a) * sin^2(a) = cos^2(a) * sin^2(a) + sin^2(a) * sin^2(a) = (cos^2(a) + sin^2(a)) * sin^2(a) = sin^2(a)