Question

[Mai anh Le]

Giải phương trình: \(\frac{x+1}{58}\)+\(\frac{x+2}{57}\)=\(\frac{x+3}{56}\)+\(\frac{x+4}{55}\)

Answer 1

[Le Tran Bach Kha]

Giải phương trình:

\(\frac{x+1}{58}+\frac{x+2}{57}=\frac{x+3}{56}+\frac{x+4}{55}\)

\(\Leftrightarrow\left(\frac{x+1}{58}+1\right)+\left(\frac{x+2}{57}+1\right)=\left(\frac{x+3}{56}+1\right)+\left(\frac{x+4}{55}+1\right)\)

\(\Leftrightarrow\frac{x+59}{58}+\frac{x+59}{57}-\frac{x+59}{56}-\frac{x+59}{55}=0\)

\(\Leftrightarrow\left(x+59\right)\left(\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}\right)=0\)

\(\Leftrightarrow x+59=0\) \(\left(\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}\ne0\right)\)

\(\Leftrightarrow x=-59\)

Vậy : \(S=\left\{-59\right\}\)

Answer 2

[Trương Huy Hoàng]

\(\frac{x+1}{58}+\frac{x+2}{57}=\frac{x+3}{56}+\frac{x+4}{55}\)

\(\Leftrightarrow\) \(\frac{x+1}{58}+1+\frac{x+2}{57}+1=\frac{x+3}{56}+1+\frac{x+4}{55}+1\)

\(\Leftrightarrow\) \(\frac{x+59}{58}+\frac{x+59}{57}=\frac{x+59}{56}+\frac{x+59}{55}\)

\(\Leftrightarrow\) \(\frac{x+59}{58}+\frac{x+59}{57}-\frac{x+59}{56}-\frac{x+59}{55}=0\)

\(\Leftrightarrow\) (x + 59)(\(\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}\)) = 0

\(\Leftrightarrow\) x + 59 = 0

\(\Leftrightarrow\) x = -59

Vậy S = {-59}

Chúc bn học tốt!!