Question

[Nguyen vu hoang minh]

Giai phuong trinh 

x+1/99  +  x+2/98  +   x+3/97=   x+4/96  +  x+5/95  +     x+10/90

Answer 1

[Trịnh Quỳnh Nhi]

Ta có x+1/99 + x+2/98 + x+3/97 = x+4/96 + x+5/95 + x+10/90

=> x+1/99 + x+2/98 + x+3/97 - x+4/96 - x+5/95 - x+10/90=0

=> (x+1/99 + 1) + (x+2/98 + 1) + (x+3/97 +1) - (x+4/96 + 1) - (x+5/95 + 1) - (x+10/90 + 1) = 0

=> x+100/99 + x+100/98 + x+100/97 - x+100/96 - x+100/95 - x+100/90 =0

=> (x+100)(1/99+1/98+1/97-1/96-1/95-1/90) = 0

Mà 1/99+1/98+1/97-1/96-1/95-1/90 khác 0

=> x+100=0 => x=-100

Vậy phương trình có nghiệm là x=-100

Answer 2

[ɱ√ρ︵ʙᴇsт➻❥ɴᴀκᴀʀoтн★彡]

\(\frac{x+1}{99}+\frac{x+2}{98}+\frac{x+3}{97}=\frac{x+4}{96}+\frac{x+5}{95}+\frac{x+10}{99}\)

\(\Leftrightarrow\frac{x+1}{99}+1+\frac{x+2}{98}+1+\frac{x+3}{97}+1-\left(\frac{x+4}{96}+1+\frac{x+5}{95}+1+\frac{x+10}{99}+1\right)=0\)

\(\Leftrightarrow\frac{x+100}{99}+\frac{x+100}{98}+\frac{x+100}{97}-\left(\frac{x+100}{96}+\frac{x+100}{95}+\frac{x+100}{90}\right)=0\)

\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}-\frac{1}{96}-\frac{1}{95}-\frac{1}{90}\right)=0\)

Mà\(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}-\frac{1}{96}-\frac{1}{95}-\frac{1}{90}\ne0\)

\(\Rightarrow x+100=0\Rightarrow x=-100\)