Ответы
Ответ дал:
1
х - 1 = 1 или х - 1 = 8
х = 2 или = 9
Ответ: 2; 9.
Ответ дал:
4
Воспользуемся формулой: ![(a+b)^3=a^3+b^3+3ab(a+b) (a+b)^3=a^3+b^3+3ab(a+b)](https://tex.z-dn.net/?f=%28a%2Bb%29%5E3%3Da%5E3%2Bb%5E3%2B3ab%28a%2Bb%29)
![\sqrt[3]{x-1} + \sqrt[3]{10-x} =3 \sqrt[3]{x-1} + \sqrt[3]{10-x} =3](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7Bx-1%7D+%2B+%5Csqrt%5B3%5D%7B10-x%7D+%3D3)
![( \sqrt[3]{x-1} + \sqrt[3]{10-x})^3 =3^3 ( \sqrt[3]{x-1} + \sqrt[3]{10-x})^3 =3^3](https://tex.z-dn.net/?f=%28+%5Csqrt%5B3%5D%7Bx-1%7D+%2B+%5Csqrt%5B3%5D%7B10-x%7D%29%5E3+%3D3%5E3)
![x-1+10-x+3 \sqrt[3]{(x-1)(10-x)} *( \sqrt[3]{x-1} + \sqrt[3]{10-x})=27 x-1+10-x+3 \sqrt[3]{(x-1)(10-x)} *( \sqrt[3]{x-1} + \sqrt[3]{10-x})=27](https://tex.z-dn.net/?f=x-1%2B10-x%2B3+%5Csqrt%5B3%5D%7B%28x-1%29%2810-x%29%7D+%2A%28+%5Csqrt%5B3%5D%7Bx-1%7D+%2B+%5Csqrt%5B3%5D%7B10-x%7D%29%3D27)
учитывая, что
, то ![x-1+10-x+3 \sqrt[3]{(x-1)(10-x)} *3=27 x-1+10-x+3 \sqrt[3]{(x-1)(10-x)} *3=27](https://tex.z-dn.net/?f=x-1%2B10-x%2B3+%5Csqrt%5B3%5D%7B%28x-1%29%2810-x%29%7D+%2A3%3D27)
![9 \sqrt[3]{(x-1)(10-x)}=18 9 \sqrt[3]{(x-1)(10-x)}=18](https://tex.z-dn.net/?f=9+%5Csqrt%5B3%5D%7B%28x-1%29%2810-x%29%7D%3D18)
![\sqrt[3]{(x-1)(10-x)}=2 \sqrt[3]{(x-1)(10-x)}=2](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B%28x-1%29%2810-x%29%7D%3D2)
![( \sqrt[3]{(x-1)(10-x)})^3=2^3 ( \sqrt[3]{(x-1)(10-x)})^3=2^3](https://tex.z-dn.net/?f=%28+%5Csqrt%5B3%5D%7B%28x-1%29%2810-x%29%7D%29%5E3%3D2%5E3)
![(x-1)(10-x)}=8 (x-1)(10-x)}=8](https://tex.z-dn.net/?f=+%28x-1%29%2810-x%29%7D%3D8)
![- x^{2} +10x+x-10-8=0 - x^{2} +10x+x-10-8=0](https://tex.z-dn.net/?f=-+x%5E%7B2%7D+%2B10x%2Bx-10-8%3D0)
![- x^{2} +11x-18=0 - x^{2} +11x-18=0](https://tex.z-dn.net/?f=-+x%5E%7B2%7D+%2B11x-18%3D0)
![x^{2} -11x+18=0 x^{2} -11x+18=0](https://tex.z-dn.net/?f=+x%5E%7B2%7D+-11x%2B18%3D0)
![D=121-72=49 D=121-72=49](https://tex.z-dn.net/?f=D%3D121-72%3D49)
![x_1=2 x_1=2](https://tex.z-dn.net/?f=x_1%3D2)
![x_2=9 x_2=9](https://tex.z-dn.net/?f=x_2%3D9)
Ответ: 2; 9
учитывая, что
Ответ: 2; 9
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