If a : b = 3 : $\sqrt{5}$, then the value of (2a + b) : (3a - 2b) is :
Answer & explanation
Correct answer: option 4
Here,
A : B
3 : \(\sqrt { 5}\)
⇒ 3k , k\(\sqrt { 5}\)
⇒ 2a + b = 6k + k\(\sqrt { 5}\)
⇒ 3a - 2b = 9k - 2k\(\sqrt { 5}\)
⇒ ( 6k + k\(\sqrt { 5}\)) : (9k - 2k\(\sqrt { 5}\))
⇒ ( 6k + k\(\sqrt { 5}\))(9k - 2k\(\sqrt { 5}\)) : (\( {9 }^{2 } \) - 20)
⇒ (64 + 21\(\sqrt { 5}\))\(\frac{1}{61}\)