\frac{1.2x {}^{2} = xy}{0.36x {}^{2} = 0.25y {}^{2} } = \frac{20x}{6x + 5y}0.36x2=0.25y21.2x2=xy​=6x+5y20x​ преобразуйте и докажите тождество

буду очень благодарна​

1)(0,5-2х)(2х+0,5)+(0,7+х)^2=0,92-0,1х

0.25-4x^2+0.49+1.4x+x^2-0.92+0.1x=0 |*100

25-400x^2+49+140x+100x^2-92+10x=0

-300x+150x-18=0 |3

-100x+50x-6=0

D=2500-2400=100

x1=-50+10/-200=40/200=20/100=0.2

x2=-50-10/-200=60/200=0.3

2)х^2-х+3/4=0 |*4

4x^2-4x+3=0

D=16-48=-32  корней нет

3)-0,04+х^2=0

x^2=0.04

x1=0.2

x2=-0.2

5)х^2+3,2х-9=0 |*10

10x^2+32x-90=0

D=1024+3600=4624   68

x1=-32+68/20=1.8

x2=-32-68/20=-5

4)1/6х^2-х+3/4=0 |*12

2x^2-12x+9=0

D=144-72=72

x1=12+sqrt72/4=12+6sqrt2/4=6(2+sqrt2)/4=6+3sqrt2/4

x2=12-sqrt72/4=6-3sqrt2/4

sqrt - квадратный корень

sin^2x+2sincosx-3cos^2x=0 | /cos^2x

tg^2x+2tgx-3=0

tgx=y

y^2+2y-3=0

y=1

y=-3

Найдем х :

1)tgx=1

x=pi/4+pik . k=z

2)tgx=-3

x=arctg(-3)+pik . k=z

sinx/2+cosx/2+sinx/2cosx/2=1 |/cosx/2

tgx/2+1+sinx/2=1

tgx/2+sinx/2=0

(sinx/2+sinx/2*cosx/2)/cosx/2=0

одз:

1)sinx/2+sinx/2*cosx/2=0

sinx/2(1+cosx/2)=0

1.sinx/2=0

x/2=pik

x=2pik. k=z

2.cosx/2=-1

x/2=pi/2+pik

x=pi+2pik . k=z

2)cosx/2≠0

x≠pi/2+pik . k=z

ответ:x=pik . k=z

sinxcosx-sin^2x+sinx-cosx=0  

sinx(cosx-sinx)-(cosx-sinx)=0

(cosx-sinx)(sinx-1)=0

1)cosx-sinx=0 |/sinx

ctgx=1

x=pi/4+pik . k=z

2)sinx-1=0

sinx=1

x=pi/2+2pik . k=z