Question

Nghiêm của PT :\(\frac{x-12}{77}+\frac{x-11}{78}=\frac{x-74}{15}+\frac{x-13}{16}\)

Answer 1

Ta có: \(\frac{x-12}{77}+\frac{x-11}{78}=\frac{x-74}{15}=\frac{x-73}{16}\)

\(\Rightarrow\left(\frac{x-12}{77}-1\right)+\left(\frac{x-11}{78}-1\right)=\left(\frac{x-74}{15}-1\right)+\left(\frac{x-73}{16}-1\right)\)

\(\Rightarrow\frac{x-89}{77}+\frac{x-89}{78}-\frac{x-89}{15}-\frac{x-89}{16}=0\)

\(\Rightarrow\left(x-89\right)\left(\frac{1}{77}+\frac{1}{78}-\frac{1}{15}-\frac{1}{16}\right)=0\)

Mà \(\frac{1}{77}+\frac{1}{78}-\frac{1}{15}-\frac{1}{16}\ne0\)

\(\Rightarrow x-89=0\)

\(\Rightarrow x=89\)

Vậy x = 89