Question

Найдите корни уравнения:

Answer 1

$\displaystyle x + \frac{4}{21} =\frac{2}{3} +\frac{2}{7}\\\\x+\frac{4}{21}=\frac{7*2}{7*3}+\frac{3*2}{3*7}\\\\x+\frac{4}{21}=\frac{14}{21}+\frac{6}{21}\\\\ x+\frac{4}{21}=\frac{20}{21}\\\\x=\frac{20}{21}-\frac{4}{21}\\\\x=\frac{16}{21}$

проверка:

$\displaystyle \frac{16}{21}+\frac{4}{21}=\frac{2}{3}+\frac{2}{7}\\\\ \frac{20}{21}=\frac{14+6}{21}\\\\ \frac{20}{21}=\frac{20}{21}$

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$\displaystyle (\frac{4}{5}-x)+\frac{13}{20}=\frac{7}{10}\\\\\frac{4}{5}-x=\frac{7}{10}-\frac{13}{20}\\\\\frac{4}{5}-x=\frac{7*2}{10*2}-\frac{13}{20}\\\\ \frac{4}{5}-x=\frac{14}{20}-\frac{13}{20}\\\\ \frac{4}{5}-x=\frac{1}{20}\\\\-x=\frac{1}{20}-\frac{4}{5}\\\\-x=\frac{1}{20}-\frac{4*4}{4*5}\\\\ -x=\frac{1}{20}-\frac{16}{20}\\\\ -x=-\frac{3}{4}\\\\x=\frac{3}{4}$

проверка: $\displaystyle (\frac{4}{5}-\frac{3}{4})+\frac{13}{20}=\frac{16-15}{20}+\frac{13}{20}=\frac{1}{20}+\frac{13}{20}=\frac{14}{20}=\frac{7*2}{10*2}=\frac{7}{10}\\\\\frac{7}{10}=\frac{7}{10}$