Question

[Lê Quý Trung]

Giải phương trình:

\(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

Answer 1

[Thắng Nguyễn]

\(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

\(\Leftrightarrow\frac{x+1}{94}+1+\frac{x+2}{93}+1+\frac{x+3}{92}+1=\frac{x+4}{91}+1+\frac{x+5}{90}+1+\frac{x+6}{89}+1\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}=\frac{x+95}{91}+\frac{x+95}{90}+\frac{x+95}{89}\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}-\frac{x+95}{91}-\frac{x+95}{90}-\frac{x+95}{89}=0\)

\(\Leftrightarrow\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)

\(\Leftrightarrow x+95=0\).Do \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\ne0\)

\(\Leftrightarrow x=-95\)

Answer 2

[TẠ THỊ NGOAN]

(x+1)/94 + ( x+2)/93 + ( x+3)/92.......

= ................ + ( x+6)/89 
<=> (x+1)/94 + 1 + ( x+2)/93 +1 .........

=.............. cộng 1 nhá 
<=> (x+95)/94 + ( x+96) / 93 + ( x+95)/92

= ( x+95)/91 + ( x+95)/90 + ( x+95)/89 
<=> ( x+95) ( 1/94 +1/93 +1/92 )

= ( x+95) ( 1/91 +1/90 +1/89) 
<=> ( x+95) ( 1/94 +1/93 +1/92 - 1/91 - 1/90 - 1/89 ) 
<=> x+95 =0 
<=>x = -95 
Vậy :x = -95