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а) ![frac{x^{2}+1}{x}+ frac{x}{x^{2}+1}= frac{5}{2} frac{x^{2}+1}{x}+ frac{x}{x^{2}+1}= frac{5}{2}](https://tex.z-dn.net/?f=+frac%7Bx%5E%7B2%7D%2B1%7D%7Bx%7D%2B+frac%7Bx%7D%7Bx%5E%7B2%7D%2B1%7D%3D+frac%7B5%7D%7B2%7D)
![frac{(x^{2}+1)^{2}+x^{2}}{x*(x^{2}+1)}= frac{5}{2} frac{(x^{2}+1)^{2}+x^{2}}{x*(x^{2}+1)}= frac{5}{2}](https://tex.z-dn.net/?f=+frac%7B%28x%5E%7B2%7D%2B1%29%5E%7B2%7D%2Bx%5E%7B2%7D%7D%7Bx%2A%28x%5E%7B2%7D%2B1%29%7D%3D+frac%7B5%7D%7B2%7D)
![frac{x^{4}+3x^{2}+1}{x^{3}+x}= frac{5}{2} frac{x^{4}+3x^{2}+1}{x^{3}+x}= frac{5}{2}](https://tex.z-dn.net/?f=+frac%7Bx%5E%7B4%7D%2B3x%5E%7B2%7D%2B1%7D%7Bx%5E%7B3%7D%2Bx%7D%3D+frac%7B5%7D%7B2%7D)
![2x^{4}+6x^{2}+2=5x^{3}+5x 2x^{4}+6x^{2}+2=5x^{3}+5x](https://tex.z-dn.net/?f=2x%5E%7B4%7D%2B6x%5E%7B2%7D%2B2%3D5x%5E%7B3%7D%2B5x)
![2x^{4}-5x^{3}+6x^{2}-5x+2=0 2x^{4}-5x^{3}+6x^{2}-5x+2=0](https://tex.z-dn.net/?f=2x%5E%7B4%7D-5x%5E%7B3%7D%2B6x%5E%7B2%7D-5x%2B2%3D0)
![2x^{4}-5x^{3}+6x^{2}-5x+2=(x-1)(2x^{3}-3x^{2}+3x-2)=0 2x^{4}-5x^{3}+6x^{2}-5x+2=(x-1)(2x^{3}-3x^{2}+3x-2)=0](https://tex.z-dn.net/?f=2x%5E%7B4%7D-5x%5E%7B3%7D%2B6x%5E%7B2%7D-5x%2B2%3D%28x-1%29%282x%5E%7B3%7D-3x%5E%7B2%7D%2B3x-2%29%3D0)
![(x-1)(x-1)(2x^{2}-x+2)=0 (x-1)(x-1)(2x^{2}-x+2)=0](https://tex.z-dn.net/?f=%28x-1%29%28x-1%29%282x%5E%7B2%7D-x%2B2%29%3D0)
1)![x_{1}=1 x_{1}=1](https://tex.z-dn.net/?f=x_%7B1%7D%3D1)
2)
- нет корней
Ответ: 1
в)![(2x^{2}-4x+1)(2x^{2}+2x+1)+5x^{2}=0 (2x^{2}-4x+1)(2x^{2}+2x+1)+5x^{2}=0](https://tex.z-dn.net/?f=%282x%5E%7B2%7D-4x%2B1%29%282x%5E%7B2%7D%2B2x%2B1%29%2B5x%5E%7B2%7D%3D0)
![4x^{4}+4x^{3}+2x^{2}-8x^{3}-8x^{2}-4x+2x^{2}+2x+1+5x^{2}=0 4x^{4}+4x^{3}+2x^{2}-8x^{3}-8x^{2}-4x+2x^{2}+2x+1+5x^{2}=0](https://tex.z-dn.net/?f=4x%5E%7B4%7D%2B4x%5E%7B3%7D%2B2x%5E%7B2%7D-8x%5E%7B3%7D-8x%5E%7B2%7D-4x%2B2x%5E%7B2%7D%2B2x%2B1%2B5x%5E%7B2%7D%3D0)
![4x^{4}-4x^{3}+x^{2}-2x+1=0 4x^{4}-4x^{3}+x^{2}-2x+1=0](https://tex.z-dn.net/?f=4x%5E%7B4%7D-4x%5E%7B3%7D%2Bx%5E%7B2%7D-2x%2B1%3D0)
![4x^{4}-4x^{3}+x^{2}-2x+1=(x-1)(4x^{3}+x-1)=0 4x^{4}-4x^{3}+x^{2}-2x+1=(x-1)(4x^{3}+x-1)=0](https://tex.z-dn.net/?f=4x%5E%7B4%7D-4x%5E%7B3%7D%2Bx%5E%7B2%7D-2x%2B1%3D%28x-1%29%284x%5E%7B3%7D%2Bx-1%29%3D0)
1)![x_{1}=1 x_{1}=1](https://tex.z-dn.net/?f=x_%7B1%7D%3D1)
2)![4x^{3}+x-1=0 4x^{3}+x-1=0](https://tex.z-dn.net/?f=4x%5E%7B3%7D%2Bx-1%3D0)
![x_{2}=0.5 x_{2}=0.5](https://tex.z-dn.net/?f=x_%7B2%7D%3D0.5)
1)
2)
Ответ: 1
в)
1)
2)
Ответ дал:
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spasiba
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