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2.
![49 {x}^{2} - 81 {y}^{2} \ = (7x - 9y)(7x + 9y) 49 {x}^{2} - 81 {y}^{2} \ = (7x - 9y)(7x + 9y)](https://tex.z-dn.net/?f=49+%7Bx%7D%5E%7B2%7D++-+81+%7By%7D%5E%7B2%7D+++%5C+%3D+%287x+-+9y%29%287x+%2B+9y%29+)
![frac{1}{64} {x}^{2} - 121 = \ (frac{1}{8} x - 11)( frac{1}{8} x + 11) frac{1}{64} {x}^{2} - 121 = \ (frac{1}{8} x - 11)( frac{1}{8} x + 11)](https://tex.z-dn.net/?f=+frac%7B1%7D%7B64%7D++%7Bx%7D%5E%7B2%7D++-+121+%3D++%5C++%28frac%7B1%7D%7B8%7D+x+-+11%29%28+frac%7B1%7D%7B8%7D+x+%2B+11%29)
![frac{1}{9} {x}^{2} - frac{4}{16} {y}^{2} = \ ( frac{1}{3} x - frac{2}{4} y)( frac{1}{3} x + frac{2}{4} y) frac{1}{9} {x}^{2} - frac{4}{16} {y}^{2} = \ ( frac{1}{3} x - frac{2}{4} y)( frac{1}{3} x + frac{2}{4} y)](https://tex.z-dn.net/?f=+frac%7B1%7D%7B9%7D++%7Bx%7D%5E%7B2%7D++-++frac%7B4%7D%7B16%7D++%7By%7D%5E%7B2%7D++%3D++%5C+%28+frac%7B1%7D%7B3%7D+x+-++frac%7B2%7D%7B4%7D+y%29%28+frac%7B1%7D%7B3%7D+x+%2B++frac%7B2%7D%7B4%7D+y%29)
3.
![4 {y}^{2} + 81 = 0 4 {y}^{2} + 81 = 0](https://tex.z-dn.net/?f=4+%7By%7D%5E%7B2%7D++%2B+81+%3D+0+)
Поскольку левая часть всегда >0 уравнение не имеет решений
![28 - {x}^{2} = 3 \ {x}^{2} = 28 - 3 = 25 \ x1 =5 \ x2 = - 5 28 - {x}^{2} = 3 \ {x}^{2} = 28 - 3 = 25 \ x1 =5 \ x2 = - 5](https://tex.z-dn.net/?f=28+-++%7Bx%7D%5E%7B2%7D++%3D+3+%5C++%7Bx%7D%5E%7B2%7D++%3D+28+-+3+%3D+25+%5C+x1+%3D5+%5C+x2+%3D++-+5)
![4z - 64z {}^{2} =0 \ 4z(1 - 16z) = 0 \ 4z = 0 \ z1 = 0 4z - 64z {}^{2} =0 \ 4z(1 - 16z) = 0 \ 4z = 0 \ z1 = 0](https://tex.z-dn.net/?f=4z+-+64z+%7B%7D%5E%7B2%7D++%3D0+%5C+4z%281+-+16z%29+%3D+0+%5C+4z+%3D+0+%5C+z1+%3D+0)
![1 - 16z = 0 \ 16z = 1 \ z2 = frac{1}{16} 1 - 16z = 0 \ 16z = 1 \ z2 = frac{1}{16}](https://tex.z-dn.net/?f=1+-+16z+%3D+0+%5C+16z+%3D+1+%5C+z2+%3D++frac%7B1%7D%7B16%7D+)
![{y}^{2} - 19 = 0 \ {y}^{2} = 19 \ y1 = - sqrt{19} \ y2 = sqrt{19} {y}^{2} - 19 = 0 \ {y}^{2} = 19 \ y1 = - sqrt{19} \ y2 = sqrt{19}](https://tex.z-dn.net/?f=+%7By%7D%5E%7B2%7D++-+19+%3D+0+%5C++%7By%7D%5E%7B2%7D++%3D+19+%5C+y1+%3D+++-++sqrt%7B19%7D++%5C+y2+%3D++sqrt%7B19%7D+)
![{z}^{2} - 5 = 0 \ {z}^{2} = 5 \ z1 = sqrt{5 } \ x2 = - sqrt{5} {z}^{2} - 5 = 0 \ {z}^{2} = 5 \ z1 = sqrt{5 } \ x2 = - sqrt{5}](https://tex.z-dn.net/?f=+%7Bz%7D%5E%7B2%7D++-+5+%3D+0+%5C++%7Bz%7D%5E%7B2%7D++%3D+5+%5C+z1+%3D++sqrt%7B5+%7D++%5C+x2+%3D++-++sqrt%7B5%7D+)
4.
![25 = {5}^{2} \ 169 = {13}^{2} \ 6400 = {80}^{2} 25 = {5}^{2} \ 169 = {13}^{2} \ 6400 = {80}^{2}](https://tex.z-dn.net/?f=25+%3D++%7B5%7D%5E%7B2%7D++%5C+169+%3D++%7B13%7D%5E%7B2%7D++%5C+6400+%3D++%7B80%7D%5E%7B2%7D+)
![17 = sqrt{17} \ 9 = {3}^{2} \ 90000 = {300}^{2} \ 15 = sqrt{15} 17 = sqrt{17} \ 9 = {3}^{2} \ 90000 = {300}^{2} \ 15 = sqrt{15}](https://tex.z-dn.net/?f=17+%3D++sqrt%7B17%7D++%5C+9+%3D++%7B3%7D%5E%7B2%7D++%5C+90000+%3D++%7B300%7D%5E%7B2%7D++%5C+15+%3D++sqrt%7B15%7D+)
5.
![- frac{24}{7} + 1 frac{2}{21} = - 3 frac{3}{7} + 1 frac{2}{21} = \ - 3 frac{9}{21} + 1 frac{2}{21} = - 2 frac{7}{21} = - 2 frac{1}{3} - frac{24}{7} + 1 frac{2}{21} = - 3 frac{3}{7} + 1 frac{2}{21} = \ - 3 frac{9}{21} + 1 frac{2}{21} = - 2 frac{7}{21} = - 2 frac{1}{3}](https://tex.z-dn.net/?f=+-++frac%7B24%7D%7B7%7D++%2B+1+frac%7B2%7D%7B21%7D++%3D++-+3+frac%7B3%7D%7B7%7D++%2B+1+frac%7B2%7D%7B21%7D++%3D++%5C++-+3+frac%7B9%7D%7B21%7D++%2B+1+frac%7B2%7D%7B21%7D++%3D++-+2+frac%7B7%7D%7B21%7D++%3D++-+2+frac%7B1%7D%7B3%7D+)
![- 1 frac{2}{3} times ( - 2 frac{1}{3} ) = frac{5}{3} times frac{7}{3} = frac{35}{9} = \ 3 frac{8}{9} - 1 frac{2}{3} times ( - 2 frac{1}{3} ) = frac{5}{3} times frac{7}{3} = frac{35}{9} = \ 3 frac{8}{9}](https://tex.z-dn.net/?f=+-+1+frac%7B2%7D%7B3%7D++times+%28+-+2+frac%7B1%7D%7B3%7D+%29+%3D++frac%7B5%7D%7B3%7D++times++frac%7B7%7D%7B3%7D++%3D++frac%7B35%7D%7B9%7D++%3D++%5C+3+frac%7B8%7D%7B9%7D+)
2)
![- 1 frac{1}{14} - 2 frac{2}{35} = - 1 frac{5}{70} - 2 frac{4}{70} = \ - 2 frac{4}{70} - 1 frac{5}{70} = - 1 frac{74}{70} - 1 frac{5}{70} = - 1 frac{1}{14} - 2 frac{2}{35} = - 1 frac{5}{70} - 2 frac{4}{70} = \ - 2 frac{4}{70} - 1 frac{5}{70} = - 1 frac{74}{70} - 1 frac{5}{70} =](https://tex.z-dn.net/?f=+-+1+frac%7B1%7D%7B14%7D++-+2+frac%7B2%7D%7B35%7D++%3D++-+1+frac%7B5%7D%7B70%7D++-+2+frac%7B4%7D%7B70%7D++%3D++%5C++-+2+frac%7B4%7D%7B70%7D++-+1+frac%7B5%7D%7B70%7D++%3D++-+1+frac%7B74%7D%7B70%7D++-+1+frac%7B5%7D%7B70%7D++%3D+)
![= - 2 frac{79}{70} = - 3 frac{9}{70} \ - 2 frac{5}{7} div ( - 3 frac{9}{70} ) = frac{19}{7} div frac{219}{70} = - 2 frac{79}{70} = - 3 frac{9}{70} \ - 2 frac{5}{7} div ( - 3 frac{9}{70} ) = frac{19}{7} div frac{219}{70}](https://tex.z-dn.net/?f=+%3D++-+2+frac%7B79%7D%7B70%7D++%3D++-+3+frac%7B9%7D%7B70%7D++%5C++-+2+frac%7B5%7D%7B7%7D++div+%28+-+3+frac%7B9%7D%7B70%7D+%29+%3D++frac%7B19%7D%7B7%7D++div++frac%7B219%7D%7B70%7D+)
![frac{19}{7} times frac{70}{219} = frac{190}{219} frac{19}{7} times frac{70}{219} = frac{190}{219}](https://tex.z-dn.net/?f=+frac%7B19%7D%7B7%7D++times++frac%7B70%7D%7B219%7D++%3D++frac%7B190%7D%7B219%7D+)
3.
Поскольку левая часть всегда >0 уравнение не имеет решений
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