Question

[Thu Hà Nguyễn]

Tìm x: \(\frac{x-241}{17}+\frac{x-220}{19}+\frac{x-195}{21}+\frac{x-166}{23}=10\)

Answer 1

[Hoang Hung Quan]

Giải:

\(\frac{x-241}{17}+\frac{x-220}{19}+\frac{x-195}{21}+\frac{x-166}{23}=10\)

\(\Rightarrow\left(\frac{x-241}{17}-1\right)+\left(\frac{x-220}{19}-2\right)+\left(\frac{x-195}{21}-3\right)+\left(\frac{x-166}{23}-4\right)\)

\(=10-1-2-3-4=0\)

\(\Rightarrow\frac{x-258}{17}+\frac{x-258}{19}+\frac{x-258}{21}+\frac{x-258}{23}=0\)

\(\Rightarrow\left(x-258\right)\left(\frac{1}{17}+\frac{1}{19}+\frac{1}{21}+\frac{1}{23}\right)=0\)

\(\Rightarrow x-258=0\)

\(\Leftrightarrow x=258\)

Answer 2

[Bùi Thị Hải Châu]

\(\frac{\text{x−241}}{17}+\frac{220}{19}+\frac{x−195}{21}+\frac{x−166}{23}=10\)

\(\Rightarrow\left[\frac{\left(x-241\right)}{17-1}\right]+\left[\frac{\left(x-220\right)}{19-2}\right]+\left[\frac{\left(x-195\right)}{21-3}\right]+\left[\frac{\left(x-166\right)}{23-4}\right]=10-1-2-3-4\)

\(\left(\text{Cộng 2 vế cho -1 - 2 - 3 - 4}\right)\)

\(\Rightarrow\frac{\left(x-258\right)}{17}+\frac{\left(x-258\right)}{19}+\frac{\left(x-258\right)}{21}+\frac{\left(x-258\right)}{23}=0\)

\(\Rightarrow\left(x-258\right).\left(\frac{1}{17}+\frac{1}{19}+\frac{1}{21}+\frac{1}{23}\right)=0\)

\(\Rightarrow x-258=0\Rightarrow x=258\)