![x^{2} - 8(x+1) \sqrt{x} +18x+1=0 \\ (x^{2} +2x+1 )+ 16x - 8(x+1) \sqrt{x} = 0 \\ (x+1)^{2} - 8(x+1) \sqrt{x} + 16 x= 0 \\ (x+1)^{2} - 2*4*(x+1) \sqrt{x} + (4 \sqrt{x} )^{2}= 0 \\ ((x+1)- 4\sqrt{x} )^{2}= 0 \\ x+1 - 4\sqrt{x} =0 \\ ](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20-%208%28x%2B1%29%20%5Csqrt%7Bx%7D%20%2B18x%2B1%3D0%20%5C%5C%20%0A%20%28x%5E%7B2%7D%20%2B2x%2B1%20%29%2B%2016x%20%20-%208%28x%2B1%29%20%5Csqrt%7Bx%7D%20%3D%200%20%5C%5C%20%0A%28x%2B1%29%5E%7B2%7D%20-%20%208%28x%2B1%29%20%5Csqrt%7Bx%7D%20%2B%2016%20x%3D%200%20%5C%5C%0A%28x%2B1%29%5E%7B2%7D%20-%20%202%2A4%2A%28x%2B1%29%20%5Csqrt%7Bx%7D%20%2B%20%284%20%5Csqrt%7Bx%7D%20%29%5E%7B2%7D%3D%200%20%5C%5C%0A%28%28x%2B1%29-%204%5Csqrt%7Bx%7D%20%29%5E%7B2%7D%3D%200%20%5C%5C%0Ax%2B1%20-%204%5Csqrt%7Bx%7D%20%3D0%20%5C%5C%20%0A)
Замена:
![\sqrt{x} = t \ \textgreater \ 0](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%3D%20t%20%5C%20%5Ctextgreater%20%5C%20%200)
![t^{2} - 4t+1 =0 \\ D=16 - 4 = 12 \\ t_{1} = \frac{4+2 \sqrt{3} }{2} = 2+ \sqrt{3} \\ t_{2} = \frac{4-2 \sqrt{3} }{2} = 2- \sqrt{3} \\ ](https://tex.z-dn.net/?f=%20%20t%5E%7B2%7D%20-%204t%2B1%20%20%3D0%20%5C%5C%0AD%3D16%20-%204%20%3D%2012%20%5C%5C%20%0A%20t_%7B1%7D%20%3D%20%20%5Cfrac%7B4%2B2%20%5Csqrt%7B3%7D%20%7D%7B2%7D%20%20%3D%202%2B%20%5Csqrt%7B3%7D%20%20%5C%5C%20%0A%20t_%7B2%7D%20%3D%20%20%5Cfrac%7B4-2%20%5Csqrt%7B3%7D%20%7D%7B2%7D%20%20%3D%202-%20%5Csqrt%7B3%7D%20%5C%5C%20%0A%20%20%20)
Переходя к переменной х, получим:
![\sqrt{x} = 2+ \sqrt{3} \\ x = (2+ \sqrt{3} ) = 4+4\sqrt{3} +3 = 7+4\sqrt{3} ](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%7D%20%3D%202%2B%20%5Csqrt%7B3%7D%20%5C%5C%20%0Ax%20%3D%20%282%2B%20%5Csqrt%7B3%7D%20%29%20%3D%204%2B4%5Csqrt%7B3%7D%20%2B3%20%3D%207%2B4%5Csqrt%7B3%7D%20%0A)
или
![\sqrt{x} = 2- \sqrt{3} \\ x = (2- \sqrt{3} ) = 4-4\sqrt{3} +3 = 7-4\sqrt{3}](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%7D%20%3D%202-%20%5Csqrt%7B3%7D%20%5C%5C%20%0Ax%20%3D%20%282-%20%5Csqrt%7B3%7D%20%29%20%3D%204-4%5Csqrt%7B3%7D%20%2B3%20%3D%207-4%5Csqrt%7B3%7D%20)
Ответ:
![7+4\sqrt{3}; 7-4\sqrt{3}.](https://tex.z-dn.net/?f=7%2B4%5Csqrt%7B3%7D%3B%20%207-4%5Csqrt%7B3%7D.)
1. Меньше.
2. х^2 = х + 2
х^2 - х - 2 = 0
D = (-1)^2 - 4 * 1 * (-2) = 9
x = (1 ± 3)/2
х1 = -1
х2 = 2
Тогда у1 = -2
у2 = 0
Ответ: (-1; -2); (2; 0)
∛216*(2/3)²=6*4/9=24/9=8/3=2⅔
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3(a-2b)^2-a(2b-a)=3(a-2b)(a-2b)+a(a-2b)=(a-2b)(3a-6b+a)=(a-2b)(4a-6b)=2(a-2b)(2a-3b)