Question

Tìm x

2x+3/5x+2=4x+5/10x+2

Answer 1

Ta có: \(\frac{2x+3}{5x+2}=\frac{4x+5}{10x+2}\)

\(\Leftrightarrow\left(2x+3\right)\left(10x+2\right)=\left(4x+5\right)\left(5x+2\right)\)

\(\Leftrightarrow20x^2+4x+30x+6=20x^2+8x+25x+10\)

\(\Leftrightarrow20x^2+34x+6=20x^2+33x+10\)

\(\Leftrightarrow20x^2+34x+6-20x^2-33x-10=0\)

\(\Leftrightarrow x-4=0\)

hay x=4

Vậy: x=4

Answer 2

\(\frac{2x+3}{5x+2}=\frac{4x+5}{10x+2}\)

\(\Leftrightarrow\frac{4x+6}{10x+4}=\frac{4x+5}{10x+2}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta được:

\(\frac{4x+6}{10x+4}=\frac{4x+5}{10x+2}=\frac{4x+6-4x-5}{10x+4-10x-2}=\frac{1}{2}\)

\(\Rightarrow4x+6=\frac{1}{2}\left(10x+4\right)\)

\(\Rightarrow4x+6=5x+2\)

\(\Rightarrow x=6-2=4\)

Vậy x = 4