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a)
![frac{x^2-x}{3}= frac{2x+4}{5} \ 5(x^2-x)=3(2x+4) \ 5x^2-5x=6x+12 \ 5x^2-5x-6x-12=0 \ 5x^2-11x-12=0 \ D=121+240=361=19^2 \ x_1= frac{11-19}{2*5} = frac{-8}{10}=-0.8 \x_2= frac{11+19}{2*5} = frac{30}{10}=3 frac{x^2-x}{3}= frac{2x+4}{5} \ 5(x^2-x)=3(2x+4) \ 5x^2-5x=6x+12 \ 5x^2-5x-6x-12=0 \ 5x^2-11x-12=0 \ D=121+240=361=19^2 \ x_1= frac{11-19}{2*5} = frac{-8}{10}=-0.8 \x_2= frac{11+19}{2*5} = frac{30}{10}=3](https://tex.z-dn.net/?f=+frac%7Bx%5E2-x%7D%7B3%7D%3D+frac%7B2x%2B4%7D%7B5%7D+++%5C+5%28x%5E2-x%29%3D3%282x%2B4%29+%5C+5x%5E2-5x%3D6x%2B12+%5C+5x%5E2-5x-6x-12%3D0+%5C+5x%5E2-11x-12%3D0+%5C+D%3D121%2B240%3D361%3D19%5E2+%5C+x_1%3D+frac%7B11-19%7D%7B2%2A5%7D+%3D+frac%7B-8%7D%7B10%7D%3D-0.8+%5Cx_2%3D+frac%7B11%2B19%7D%7B2%2A5%7D+%3D+frac%7B30%7D%7B10%7D%3D3+)
б)
![frac{x^2-3}{2}-6x=5 \ x^2-3-6x*2=5*2 \ x^2-3-12x=10 \ x^2-3-12x-10=0 \ x^2-12x-13=0 \
D=144+52=196=14^2 \ x_1= frac{12-14}{2}= frac{-2}{2}=-1 \x_2= frac{12+14}{2}= frac{26}{2}=13 frac{x^2-3}{2}-6x=5 \ x^2-3-6x*2=5*2 \ x^2-3-12x=10 \ x^2-3-12x-10=0 \ x^2-12x-13=0 \
D=144+52=196=14^2 \ x_1= frac{12-14}{2}= frac{-2}{2}=-1 \x_2= frac{12+14}{2}= frac{26}{2}=13](https://tex.z-dn.net/?f=frac%7Bx%5E2-3%7D%7B2%7D-6x%3D5+%5C++x%5E2-3-6x%2A2%3D5%2A2+%5C+x%5E2-3-12x%3D10+%5C+x%5E2-3-12x-10%3D0+%5C+x%5E2-12x-13%3D0+%5C+%0AD%3D144%2B52%3D196%3D14%5E2+%5C+x_1%3D+frac%7B12-14%7D%7B2%7D%3D+frac%7B-2%7D%7B2%7D%3D-1+++%5Cx_2%3D+frac%7B12%2B14%7D%7B2%7D%3D+frac%7B26%7D%7B2%7D%3D13+++)
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![frac{2x^2+x}{5}= frac{4x-2}{3} \ 3(2x^2+x)=5(4x-2) \ 6x^2+3x=20x-10 \ 6x^2+3x-20x+10=0 \ 6x^2-17x+10=0 \ D=289-240=49=7^2 \ x_1= frac{17-7}{2*6} = frac{10}{12}= frac{5}{6} \ x_2= frac{17+7}{2*6} = frac{24}{12}=2 frac{2x^2+x}{5}= frac{4x-2}{3} \ 3(2x^2+x)=5(4x-2) \ 6x^2+3x=20x-10 \ 6x^2+3x-20x+10=0 \ 6x^2-17x+10=0 \ D=289-240=49=7^2 \ x_1= frac{17-7}{2*6} = frac{10}{12}= frac{5}{6} \ x_2= frac{17+7}{2*6} = frac{24}{12}=2](https://tex.z-dn.net/?f=frac%7B2x%5E2%2Bx%7D%7B5%7D%3D+frac%7B4x-2%7D%7B3%7D++%5C+3%282x%5E2%2Bx%29%3D5%284x-2%29+%5C+6x%5E2%2B3x%3D20x-10+%5C+6x%5E2%2B3x-20x%2B10%3D0+%5C+6x%5E2-17x%2B10%3D0+%5C+D%3D289-240%3D49%3D7%5E2+%5C+x_1%3D+frac%7B17-7%7D%7B2%2A6%7D+%3D+frac%7B10%7D%7B12%7D%3D+frac%7B5%7D%7B6%7D++%5C+x_2%3D+frac%7B17%2B7%7D%7B2%2A6%7D+%3D+frac%7B24%7D%7B12%7D%3D2)
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![frac{4x^2+x}{3}- frac{5x-1}{6}=frac{x^2+17}{9} \ 6(4x^2+x)-3(5x-1)=2(x^2+17) \ 24x^2+6x-15x+3=2x^2+34 \ 24x^2-9x+3-2x^2-34=0 \ 22x^2 -9x-31=0 \ D=81+2728=2809=53^2 \ x_1= frac{9-53}{2*22} = frac{-44}{44} =-1 \ x_2= frac{9+53}{2*22} = frac{62}{44} = frac{31}{22}=1 frac{9}{22} frac{4x^2+x}{3}- frac{5x-1}{6}=frac{x^2+17}{9} \ 6(4x^2+x)-3(5x-1)=2(x^2+17) \ 24x^2+6x-15x+3=2x^2+34 \ 24x^2-9x+3-2x^2-34=0 \ 22x^2 -9x-31=0 \ D=81+2728=2809=53^2 \ x_1= frac{9-53}{2*22} = frac{-44}{44} =-1 \ x_2= frac{9+53}{2*22} = frac{62}{44} = frac{31}{22}=1 frac{9}{22}](https://tex.z-dn.net/?f=frac%7B4x%5E2%2Bx%7D%7B3%7D-+frac%7B5x-1%7D%7B6%7D%3Dfrac%7Bx%5E2%2B17%7D%7B9%7D+%5C+6%284x%5E2%2Bx%29-3%285x-1%29%3D2%28x%5E2%2B17%29+%5C+24x%5E2%2B6x-15x%2B3%3D2x%5E2%2B34+%5C+24x%5E2-9x%2B3-2x%5E2-34%3D0+%5C+22x%5E2+-9x-31%3D0+%5C+D%3D81%2B2728%3D2809%3D53%5E2+%5C+x_1%3D+frac%7B9-53%7D%7B2%2A22%7D+%3D+frac%7B-44%7D%7B44%7D+%3D-1+%5C+++x_2%3D+frac%7B9%2B53%7D%7B2%2A22%7D+%3D+frac%7B62%7D%7B44%7D+%3D+frac%7B31%7D%7B22%7D%3D1++frac%7B9%7D%7B22%7D+)
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