Question

Giải phương trình:\(\frac{x+73}{27}+\frac{x+74}{26}=\frac{x+27}{73}+\frac{x+26}{74}\)

Answer 1

\(\frac{x+73}{27}+1+\frac{x+74}{26}+1=\frac{x+27}{73}+1+\frac{x+26}{74}+1\)

\(\frac{x+73+27}{27}+\frac{x+74+26}{26}=\frac{x+27+73}{73}+\frac{x+26+74}{74}\)

\(\frac{x+100}{27}+\frac{x+100}{26}=\frac{x+100}{73}+\frac{x+100}{74}\)

\(\left(x+100\right)\left(\frac{1}{27}+\frac{1}{26}-\frac{1}{73}-\frac{1}{74}\right)=0\)

mà \(\frac{1}{27}+\frac{1}{26}-\frac{1}{73}-\frac{1}{74}\ne0\)

\(\Rightarrow x+100=0\Rightarrow x=-100\)