Question

[Vương Khánh Linh]

giải phương trình: x-23/24 +x-23/25 = x-23/26 +x-23/27

Answer 1

[Nguyễn Minh Đăng]

Ta có: \(\frac{x-23}{24}+\frac{x-23}{25}=\frac{x-23}{26}+\frac{x-23}{27}\)

\(\Leftrightarrow\frac{x-23}{24}+\frac{x-23}{25}-\frac{x-23}{26}-\frac{x-23}{27}=0\)

\(\Leftrightarrow\left(x-23\right)\left(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\right)=0\)

Vì \(\hept{\begin{cases}\frac{1}{24}>\frac{1}{26}\\\frac{1}{25}>\frac{1}{27}\end{cases}}\Rightarrow\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}>0\)

\(\Rightarrow x-23=0\Leftrightarrow x=23\)

Vậy x = 23

Answer 2

[Xyz OLM]

Ta có \(\frac{x-23}{24}+\frac{x-23}{25}=\frac{x-23}{26}+\frac{x-23}{27}\)

<=> \(\frac{x-23}{24}+\frac{x-23}{25}-\frac{x-23}{26}-\frac{x-23}{27}=0\)

<=> \(\left(x-23\right)\left(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\right)=0\)

<=> x - 23 = 0 (Vì \(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\ne0\))

<=> x = 23

Vậy x = 23 là nghiệm phương trình