Correct Answer - Option 4 : 84 ∶ 11
Given:
\(\frac{2x \ + \ 3y}{3x \ + \ 5y} = \frac{18}{29}\)
Calculation:
\(\frac{2x \ + \ 3y}{3x \ + \ 5y} = \frac{18}{29}\)
⇒ 29 × (2x + 3y) = 18 × (3x + 5y)
⇒ 58x + 87y = 54x + 90y
⇒ 4x = 3y
⇒ x/y = 3/4
Now put the value of x and y in \(\frac{4x^2 \ + \ 3y^2}{3x^2 \ - \ y^2}\)
\(\frac{4 \ \times \ 3^2 \ + \ 3\ \times \ 4^2}{3\times \ 3^2 \ - \ 4^2}\)
⇒ \(\frac{4 \ \times \ 9 \ + \ 3\ \times \ 16}{3\times \ 9 \ - \ 16}\)
⇒ \(\frac{84}{11}\)
∴ The value of \(\frac{4x^2 \ + \ 3y^2}{3x^2 \ - \ y^2}\) = \(\frac{84}{11}\)
