Question

Cho \(\dfrac{3.a^2-b^2}{a^2+b^2}=\dfrac{3}{4}\)Tính \(\dfrac{a}{b}\)

Answer 1

theo bài ra ta có:

\(\dfrac{3a^2-b^2}{a^2+b^2}=\dfrac{3}{4}\\ \Rightarrow4\left(3a^2-b^2\right)=3\left(a^2+b^2\right)\\ \Rightarrow12a^2-4b^2=3a^2+3b^2\\ \Rightarrow12a^2-3a^2=3b^2+4b^2\\ \Rightarrow9a^2=7b^2\\ \Rightarrow\dfrac{a^2}{b^2}=\dfrac{7}{9}\\ \Rightarrow\dfrac{a}{b}=\sqrt{\dfrac{7}{9}}\)