Question

[Nguyễn Thị Thanh Xuân]

giúp giải toán

Answer 1

[Vũ Ngọc Thảo Nguyên]

\(\Rightarrow\left(\frac{x-97}{3}-1\right)+\left(\frac{x-96}{4}-1\right)=\left(\frac{x-95}{5}-1\right)+\left(\frac{x-94}{6}-1\right)\)

\(\Rightarrow\frac{x-100}{3}+\frac{x-100}{4}=\frac{x-100}{5}+\frac{x-100}{6}\)

\(\Rightarrow\frac{x-100}{3}+\frac{x-100}{4}-\frac{x-100}{5}-\frac{x-100}{6}=0\)

\(\Rightarrow\left(x-100\right).\frac{1}{3}+\left(x-100\right).\frac{1}{4}-\left(x-100\right).\frac{1}{5}-\left(x-100\right).\frac{1}{6}=0\)

\(\Rightarrow\left(x-100\right)\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)=0\)

\(Mà\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\ne0\)

\(\Rightarrow x-100=0\)

\(\Rightarrow x=100\)

\(\text{Vậy x=100}\)