Решение
log₂(x + y) + log(₂²) (x - y)² = 5
3^(1 + log₃ (x - y)² = 48
ОДЗ: x + y > 0
x - y > 0, x > y
log₂[(x + y)*(x - y)] = 5
3*3^[log₃ (x - y)²] = 48
(x + y)*(x - y)] = 2⁵
(x - y)² = 16
(x - y)² = 4²
x - y = - 4 не удовлетворяет ОДЗ
x - y = 4
(x + y)*( 4)= 32
x + y = 8
y = 8 - x
x - ( 8 - x) = 4
2x = 12
x = 6
y = 8 - 6 = 2
Ответ: (6;2)
A)2sin60cos20=2*√3/2cos20=√3cos20
б)2sin20cos60=2*1/2sin20=sin20
в)2cos80
г)-2sin20sin60=-2*√3/2sin20=-√3sin20
a)2sin80cos30=2*√3/2sin80=√3sin80
б)2sin30cos80=2*1/2cos80=cos80
в)2cos80cos30=2*√3/2cos80=√3сos80
г)-sin30cos80=-2*1/2cos80=-cos80
a)sin3π/5-sin2π/5=2sinπ/10cosπ/2=2sinπ/10*0=0
б)sin3π/10-sin7π/10=2sin(2π/5)cosπ/2=-2sin2π/5*0=0
sin105*cos15=1/2(sin(105-15)+sin(105+15))=1/2(sin90+sin120)= 1/2sin90+1/2sin(180-60)=1/2*1+1/2sin60=1/2+1/2*√3/2=1/2+√3/4
Ах + 8у = 20
А(3;4)
а*3 + 8*4 = 20
3а + 32 = 20
3а = -12
а = -4
Ответ: -4