Question

[Hàn Vũ Nhi]

Giải các phương trình sau : ( biến đổi đặc biệt )

a) \(\frac{x+1}{65}\) + \(\frac{x+3}{63}\)= \(\frac{x+5}{61}\)+ \(\frac{x+7}{59}\)

b) \(\frac{x+29}{31}\)- \(\frac{x+27}{33}\)= \(\frac{x+17}{43}\)- \(\frac{x+15}{45}\)

c) \(\frac{x+6}{1999}\)+ \(\frac{x+8}{1997}\)= \(\frac{x+10}{1995}\)+ \(\frac{x+12}{1993}\)

d) \(\frac{1909-x}{91}\)+ \(\frac{1907-x}{93}\)+ \(\frac{1905-x}{95}\)+ \(\frac{1903-x}{91}\)+ 4 = 0

Answer 1

[Tran Le Khanh Linh]

a, \(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+5}{61}+\frac{x+7}{59}\)

\(\Leftrightarrow\frac{x+1}{65}+\frac{x+3}{63}-\frac{x+5}{61}-\frac{x+7}{59}=0\)

\(\Leftrightarrow\frac{x+1}{65}+1+\frac{x+3}{63}+1-\left(\frac{x+5}{61}+1\right)-\left(\frac{x+7}{59}+1\right)=0\)

\(\Leftrightarrow\frac{x+66}{65}+\frac{x+66}{63}-\frac{x+66}{61}-\frac{x+66}{59}\)=0

<=> \(\left(x+66\right)\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)

<=> x+66=0 \(\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\ne0\right)\)

<=> x=-66

Answer 2

[Tran Le Khanh Linh]

các câu còn lại cũng làm tương tự nhé