(x+2)²-49=0
x²+4x+4-49=0
x²+4x-45=0
D=4²-4*1*(-45)=16+180=196, √196=14
x₁=-4+14/2=10/2=5
x₂=-4-14/2=-18/2=<span>-9</span>
![\dispaystyle (2 \sqrt{2}+5 \sqrt{5}+10+\sqrt{10})*(2 \sqrt{2}+5 \sqrt{5}-10- \sqrt{10})=\\((2 \sqrt{2}+5 \sqrt{5})+(10+ \sqrt{10}))*((2 \sqrt{2}+5 \sqrt{5})-(10+ \sqrt{10}))=\\](https://tex.z-dn.net/?f=%5Cdispaystyle+%282+%5Csqrt%7B2%7D%2B5+%5Csqrt%7B5%7D%2B10%2B%5Csqrt%7B10%7D%29%2A%282+%5Csqrt%7B2%7D%2B5+%5Csqrt%7B5%7D-10-+%5Csqrt%7B10%7D%29%3D%5C%5C%28%282+%5Csqrt%7B2%7D%2B5+%5Csqrt%7B5%7D%29%2B%2810%2B+%5Csqrt%7B10%7D%29%29%2A%28%282+%5Csqrt%7B2%7D%2B5+%5Csqrt%7B5%7D%29-%2810%2B+%5Csqrt%7B10%7D%29%29%3D%5C%5C++++++++++++)
А теперь внимательно смотрим
![\dispaystyle a^2-b^2=(a-b)(a+b)\\ a=2 \sqrt{2}+5 \sqrt{5}\\b=10+ \sqrt{10}](https://tex.z-dn.net/?f=%5Cdispaystyle+a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29%5C%5C+a%3D2+%5Csqrt%7B2%7D%2B5+%5Csqrt%7B5%7D%5C%5Cb%3D10%2B+%5Csqrt%7B10%7D+++)
продолжаем
![\dispaystyle =(2 \sqrt{2}+5 \sqrt{5})^2-(10+ \sqrt{10})^2=\\=((2 \sqrt{2})^2+2*2*5* \sqrt{2*5}+(5 \sqrt{5})^2)-(100+20 \sqrt{10}+10)=\\=(8+20 \sqrt{10}+125)-(110+20 \sqrt{10)}= 133+20 \sqrt{10}-110-20 \sqrt{10}\\=23](https://tex.z-dn.net/?f=%5Cdispaystyle+%3D%282+%5Csqrt%7B2%7D%2B5++%5Csqrt%7B5%7D%29%5E2-%2810%2B+%5Csqrt%7B10%7D%29%5E2%3D%5C%5C%3D%28%282+%5Csqrt%7B2%7D%29%5E2%2B2%2A2%2A5%2A+%5Csqrt%7B2%2A5%7D%2B%285+%5Csqrt%7B5%7D%29%5E2%29-%28100%2B20+%5Csqrt%7B10%7D%2B10%29%3D%5C%5C%3D%288%2B20+%5Csqrt%7B10%7D%2B125%29-%28110%2B20+%5Csqrt%7B10%29%7D%3D+133%2B20+%5Csqrt%7B10%7D-110-20+%5Csqrt%7B10%7D%5C%5C%3D23+++++++++)
1)а²-ас+а 2)-сm-cn+3c 3)5x²+5xy²-25x 4)4y²+4yx²-24y
Заменяешь х на у. Получается <span>у²-</span><span>17у +16=0. D=225(корень 15). Следовательно х1=17+15/2=23,5
х2=17-15/2=2
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