Question

cho 3a² - b² / a² + b² = 3/4  

tính a/b

Answer 1

Ta có: \(\dfrac{3a^2-b^2}{a^2+b^2}=\dfrac{3}{4}\)

\(\Leftrightarrow4\cdot\left(3a^2-b^2\right)=3\left(a^2+b^2\right)\)

\(\Leftrightarrow12a^2-4b^2=3a^2+3b^2\)

\(\Leftrightarrow12a^2-3a^2=3b^2+4b^2\)

\(\Leftrightarrow9a^2=7b^2\)

\(\Leftrightarrow\dfrac{a^2}{b^2}=\dfrac{7}{9}\)

hay \(\dfrac{a}{b}=\pm\dfrac{\sqrt{7}}{3}\)