-у=-10-3х х²-40х-12х²-(100+60х+9х²)+20=0
x^2-4xy-y^2=-20 х²-40х-12х²-100-60х-9х²+20=0
-20х²-100х-80=0(/-20)
у=10+3х х²+5х+4=0
x^2-4x(10+3х)-(10+3х)^2=-20 D=25-4*4=9
x=(-5+3)/2=-1
x=(-5-3)/2=-4
х=-1 х=-1
у=10+3*(-1) у=7
х=-4 х=-4
у=10+3*(-4) у=-2
ОТВЕТ: (-1;7);(-4;2)
1) sin 82° 30' cos 37° 30'
sina+sinb=2sin(a+b/2)*cos(a-b/2)
a+b/2=82,5
a-b/2=37,5
a+b=165
a-b=75
a=165-b
165-b-b=75
-2b=-90
b=45
a=120
(1/2)* 2sin 82° 30' cos 37° 30'=(sin120+sin45)/2=(sin(180-60)+sin45)/2=(sin60+sin45)/2=(sqrt(3)/2+sqrt(2)/2)/2=((sqrt(3)+sqrt(2))/2)/2=(sqrt(3)+sqrt(2))/4
2) 2sin 3a cos 4a + sin a = sin 7a
sina1+sinb=2sin(a1+b/2)*cos(a1-b/2)
a1+b/2=3a
a1-b/2=4a
a1+b=6a
a1-b=8a
a1=6a-b
6a-b-b=8a
-2b=2a
b=-a
a1=6a+a=7a
2sin 3a cos 4a + sin a = sin 7a
sin7a+sin(-a)+sina=sin7a
sin7a-sina+sina=sin7a
sin7a=sin7a
3) 4cos a/2 cos a sin 3a/2 = sin a + sin 2a + sin 3a
2*2cosa cosa/2 sin3a/2=sina + sin2a + sin3a
2*(cosa/2 + cos 3a/2)*sin3a/2=sina + sin2a + sin3a
2 cosa/2 * sin3a/2 + 2 cos3a/2 sin3a/2 = sina + sin2a + sin3a
2 cosa/2 * sin3a/2 + sin3a = sina + sin2a + sin3a
sin a + sin 2a + sin 3a = sina + sin2a + sin3a
-у=-10-3х х²-40х-12х²-(100+60х+9х²)+20=0
x^2-4xy-y^2=-20 х²-40х-12х²-100-60х-9х²+20=0
-20х²-100х-80=0(/-20)
у=10+3х х²+5х+4=0
x^2-4x(10+3х)-(10+3х)^2=-20 D=25-4*4=9
x=(-5+3)/2=-1
x=(-5-3)/2=-4
х=-1 х=-1
у=10+3*(-1) у=7
х=-4 х=-4
у=10+3*(-4) у=-2
ОТВЕТ: (-1;7);(-4;2)
1) sin 82° 30' cos 37° 30'
sina+sinb=2sin(a+b/2)*cos(a-b/2)
a+b/2=82,5
a-b/2=37,5
a+b=165
a-b=75
a=165-b
165-b-b=75
-2b=-90
b=45
a=120
(1/2)* 2sin 82° 30' cos 37° 30'=(sin120+sin45)/2=(sin(180-60)+sin45)/2=(sin60+sin45)/2=(sqrt(3)/2+sqrt(2)/2)/2=((sqrt(3)+sqrt(2))/2)/2=(sqrt(3)+sqrt(2))/4
2) 2sin 3a cos 4a + sin a = sin 7a
sina1+sinb=2sin(a1+b/2)*cos(a1-b/2)
a1+b/2=3a
a1-b/2=4a
a1+b=6a
a1-b=8a
a1=6a-b
6a-b-b=8a
-2b=2a
b=-a
a1=6a+a=7a
2sin 3a cos 4a + sin a = sin 7a
sin7a+sin(-a)+sina=sin7a
sin7a-sina+sina=sin7a
sin7a=sin7a
3) 4cos a/2 cos a sin 3a/2 = sin a + sin 2a + sin 3a
2*2cosa cosa/2 sin3a/2=sina + sin2a + sin3a
2*(cosa/2 + cos 3a/2)*sin3a/2=sina + sin2a + sin3a
2 cosa/2 * sin3a/2 + 2 cos3a/2 sin3a/2 = sina + sin2a + sin3a
2 cosa/2 * sin3a/2 + sin3a = sina + sin2a + sin3a
sin a + sin 2a + sin 3a = sina + sin2a + sin3a