Question

tìm x biết 2x+7/6+ 13/12+21/20+31/30+43/42+57/56+73/72+91/90=10

Answer 1

Ta có: \(2x+\frac76+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}+\frac{73}{72}+\frac{91}{90}=10\)

=>\(2x+1+\frac16+1+\frac{1}{12}+\ldots+1+\frac{1}{90}=10\)

=>\(2x+8+\left(\frac16+\frac{1}{12}+\cdots+\frac{1}{90}\right)=10\)

=>\(2x+8+\left(\frac12-\frac13+\frac13-\frac14+\cdots+\frac19-\frac{1}{10}\right)=10\)

=>\(2x+8+\left(\frac12-\frac{1}{10}\right)=10\)

=>\(2x+8+\frac{4}{10}=10\)

=>\(2x=10-8-\frac{4}{10}=2-\frac{4}{10}=2-\frac25=\frac85\)

=>\(x=\frac85:2=\frac45\)