Question

Tìm a,b biết rằng :

\(\frac{1+2a}{15}=\frac{7-3a}{20}=\frac{3b}{23+7a}\)

Answer 1

TL :

Ta có : \(\frac{1+2a}{15}=\frac{7-3a}{20}=\frac{3b}{23+7a}\)

Vì \(\frac{1+2a}{15}=\frac{7-3a}{20}\)

\(\Rightarrow20\left(1+2a\right)=15\left(7-3a\right)\)

\(\Leftrightarrow20+40a=105-45a\Leftrightarrow40a+45a=105-20\)

\(\Leftrightarrow95a=95\Rightarrow a=1\)

Thay a = 1 vào phương trình  \(\frac{7-3a}{20}=\frac{3b}{23+7a}\); ta có : \(\frac{7-3.1}{20}=\frac{3b}{23+7.1}\)

\(\Leftrightarrow\frac{4}{20}=\frac{3b}{30}\Leftrightarrow\frac{1}{5}=\frac{b}{10}\Leftrightarrow5b=10\Rightarrow b=2\)

Vậy a = 1 ; b = 2

Answer 2

Có:

\(\frac{1+2a}{15}=\frac{7-3a}{20}\Leftrightarrow20\left(1+2a\right)=15\left(7-3a\right)\Rightarrow a=1\)

Thay a=1 vào\(\frac{1+2a}{15}=\frac{3b}{23+7a}=\frac{1}{5}=\frac{b}{10}\Rightarrow b=2\)