Question

 Giải phương trình:

\(\frac{x-20}{7}\)\(+\frac{x-46}{33}+\frac{x-5}{8}+\frac{x+6}{19}=0\)

 

Answer 1

             \(\frac{x-20}{7}+\frac{x-46}{33}+\frac{x-5}{8}+\frac{x+6}{19}=0\)

\(\Leftrightarrow\)\(\left(\frac{x-20}{7}+1\right)+\left(\frac{x-46}{33}+1\right)+\left(\frac{x-5}{8}-1\right)+\left(\frac{x+6}{19}-1\right)=0\)

\(\Leftrightarrow\)\(\frac{x-13}{7}+\frac{x-13}{33}+\frac{x-13}{8}+\frac{x-13}{19}=0\)

\(\Leftrightarrow\)\(\left(x-13\right)\left(\frac{1}{7}+\frac{1}{33}+\frac{1}{8}+\frac{1}{19}\right)=0\)

\(\Leftrightarrow\)\(x-13=0\)       (vi  1/7 + 1/33 + 1/8 + 1/19 \(\ne0\))

\(\Leftrightarrow\)\(x=13\)

Vậy phương trình có nghiệm là     \(x=13\)

Answer 2

pt <=> ( x-20/7 +1 ) + ( x-46/33 + 1 ) + ( x-5/8 - 1 ) + ( x+6/19 - 1 ) = 0

<=> x-13/7 + x-13/33 + x-13/8 + x-13/19 = 0

<=> (x-13).( 1/7+1/33+1/8+1/19 ) = 0

<=> x-13 = 0 ( vì 1/7+1/33+1/8+1/19 > 0 )

<=> x=13

Vậy x=13

Tk mk nha

Answer 3

\(\frac{x-20}{7}+\frac{x-46}{33}+\frac{x-5}{8}+\frac{x+6}{19}=0\)

\(\Leftrightarrow\left(\frac{x-20}{7}+1\right)+\left(\frac{x-46}{33}+1\right)+\left(\frac{x-5}{8}-1\right)+\left(\frac{x+6}{19}-1\right)=0\)

\(\Leftrightarrow\frac{x-13}{7}+\frac{x-13}{33}+\frac{x-13}{8}+\frac{x-13}{19}=0\)

\(\Leftrightarrow\left(x-13\right)\left(\frac{1}{7}+\frac{1}{33}+\frac{1}{8}+\frac{1}{19}\right)=0\)

Mà \(\frac{1}{7}+\frac{1}{33}+\frac{1}{8}+\frac{1}{19}\ne0\)

\(\Rightarrow x-13=0\Leftrightarrow x=13\)