Решите систему уравнений 1. 4 (х-у) = -2 3х-7у = - 2,5 - 2(х+у) 2. 2- 3х = 2(1-у) 4(х+у) = х - 1,5 3. - id123786620210816 от DanyaOMG 16.08.2021 16:52

Question

Алгебра: Решите систему уравнений 1. 4 (х-у) = -2 3х-7у = - 2,5 - 2(х+у) 2. 2- 3х = 2(1-у) 4(х+у) = х - 1,5 3. х/2 + у/3 = 3 х/3 + у/2 = 1/3 / - дробь

DanyaOMG · Accepted Answer

1
2(√3/2cosx-1/2sinx)=√2
cos(x+π/6)=√2/2
x+π/6=-π/4+2πn U x+π/6=π/4+2πn
x=-5π/12+2πn U x=π/12+2πn,n∈z
2
2(1/2cosx-√3/2sinx)=2cos5x
cos(x+π/3)=cos5x
5x=x+π/3+2πn U 5x=-π/3-x+2πn
4x=π/3+2πn U 6x=-π/3+2πn
x=π/12+πn/2 U x=-π/18+πn/3,n∈z
3
sin3xcos2x=sin(3x+2x)
sin3xcos2x=sin3xcos2x+sin2xcos3x
sin2xcos3x=0
sin2x=0⇒2x=πn⇒x=πn/2,n∈z
cos3x=0⇒3x=π/2+πn⇒x=π/6+πn/3,n∈z
4
sinxsin7x=sin3xsin5x
1/2[cos(7x-x)-cos(7x+x)]=1/2[cos(5x-3x)-cos(5x+3x)]
cos6x-cos8x=cos2x-cos8x
cos6x=cos2x
6x=2x+2πn U 6x=-2x+2πn
4x=2πn U 8x=2πn
x=πn/2 U x=πn/4-общий

Решите систему уравнений 1. 4 (х-у) = -2 3х-7у = - 2,5 - 2(х+у) 2. 2- 3х = 2(1-у) 4(х+у) = х - 1,5 3. х/2 + у/3 = 3 х/3 + у/2 = 1/3 / - дробь

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