Число −0,7 (является или не является) решением неравенства |x|<−0,7.

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Ответ:

Hunterxxxx

16.05.2023 06:34

$sin^{2}(x)*(tg(x)+1)=3sin(x)*(cos(x)-sin(x))+3\\sin^{2}(x)*(\frac{sin(x)}{cos(x)} +1)=3sin(x)cos(x)-3sin^{2}(x)+3\\sin^{2}(x)*\frac{sin(x)+cos(x)}{cos(x)}=\frac{3}{2}*sin(2x)-3sin^{2}(x)+3\\\frac{sin^{2}(x)*(sin(x)+cos(x))}{cos(x)}=\frac{3sin(2x)}{2}-3sin^{2}(x)+3\\\frac{sin^{3}(x)+sin^{2}(x)cos(x)}{cos(x)}=\frac{3sin(2x)}{2}-3sin^{2}(x)+3\\\frac{sin^{3}(x)+sin^{2}(x)cos(x)}{cos(x)}-\frac{3sin(2x)}{2}+3sin^{2}(x)=3\\\frac{2(sin^{3}(x)+sin^{2}(x)cos(x))-3cos(x)sin(2x)+6cos(x)sin^{2}(x)}{2cos(x)}=3\\$

$\frac{2sin^{3}(x)+2sin^{2}(x)cos(x)-3cos(x)sin(2x)+6cos(x)sin^{2}(x)}{2cos(x)}=3\\\frac{2sin^{3}(x)+8sin^{2}(x)cos(x)-3cos(x)sin(2x)}{2cos(x)}=3|*2cos(x)\\2sin^{3}(x)+8sin^{2}(x)cos(x)-3cos(x)sin(2x)=6cos(x)\\2sin^{3}(x)+8sin^{2}(x)cos(x)-3cos(x)sin(2x)-6cos(x)=0\\2sin^{3}(x)+8sin^{2}(x)cos(x)-3cos(x)*2sin(x)cos(x)-6cos(x)=0\\2sin^{3}(x)+8sin^{2}(x)cos(x)-6cos^{2}(x)sin(x)-6cos(x)=0\\2sin^{3}(x)+8sin^{2}(x)cos(x)-6(1-sin^{2}(x))sin(x)-6cos(x)=0\\$

$2sin^{3}(x)+8sin^{2}(x)cos(x)-6sin(x)+6sin^{3}(x)-6cos(x)=0\\8sin^{3}(x)+8sin^{2}(x)cos(x)-6sin(x)+6cos(x)=0\\8sin^{2}(x)*(sin(x)+cos(x))-6(sin(x)+cos(x))=0\\2(sin(x)+cos(x))*(4sin^{2}(x)-3)=0\\(sin(x)+cos(x))*(4sin^{2}(x)-3)=0$

sin(x)+cos(x) = 0 или 4sin²(x)-3 = 0

sin(x) = -cos(x) |:cos(x) 4sin²(x) = 3

tg(x) = -1 sin²(x) = 3/4

x₁ = 3π/4 + πn, n∈Z sin(x) = ±√3/2

sin(x) = -√3/2 или sin(x) = √3/2

x₂ = arcsin(-√3/2) + 2πn x₄ = arcsin(√3/2) + 2πn

x₃ = π-arcsin(-√3/2) + 2πn x₅ = π-arcsin(√3/2) + 2πn

x₂ = -π/3 + 2πn x₄ = π/3 + 2πn

x₃ = π+π/3 + 2πn x₅ = π-π/3 + 2πn

x₂ = 5π/3 + 2πn, n∈Z x₄ = π/3 + 2πn, n∈Z

x₃ = 4π/3 + 2πn, n∈Z x₅ = 2π/3 + 2πn, n∈Z

Следовательно:

x₄ = π/3 + 2πn, n∈Z,

x₅ = 2π/3 + 2πn, n∈Z

ответ: x₁ = 3π/4 + πn, n∈Z;

x₄ = π/3 + 2πn, n∈Z;

x₅ = 2π/3 + 2πn, n∈Z

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Ответ:

SAVITAR75657

07.06.2023 03:54

1) (Х + 2)*(x - 2)/ (Х - 1)(x - 2) = (x² - 4) / (Х - 1)(x - 2) = (x² - 4) / (x² - 3x + 2)
(Х + 1) (x - 1) / (Х - 2)(x - 1) = (x² - 1) / (Х - 2)(x - 1) = (x² - 1) / (x² - 3x + 2)
2) (Х - 3) (x - 3)/ (Х + 3)(x - 3) = (x - 3)² / (x² - 9)
Х*(x + 3) / (Х - 3)(x + 3) = x*(x + 3) / (x² - 9)
3) (3 + Х)(x - 3) / (Х - 5)(x - 3) = (x² - 9) / (Х - 5)(x - 3) = (x² - 9) / (x² - 8x + 15)
Х*(x - 5) / (Х - 3)(x - 5) = Х*(x - 5) / (x² - 8x + 15)
4) (Х + 1)(x + 2) /x*(x² - 4) = (x² + 3x + 2) /x*(x² - 4)
x (4 + Х) / x( x² - 4)

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