Question

2+3√5/2-3√5 = a+b =√5 solve it please​

Answer 1

Answer:

Given:

$\dfrac{2+3\sqrt5}{2-3\sqrt5} = a + \sqrt5b$

Solution:

$\implies \dfrac{2+3\sqrt5}{2-3\sqrt5}=a+\sqrt5b$

$\implies \dfrac{2+3\sqrt5}{2-3\sqrt5} \times \dfrac{2+3\sqrt5}{2+3\sqrt5} = a+\sqrt5b$

$\implies \dfrac{(2+3\sqrt5)^2}{2^2 - (3\sqrt5)^2} = a+ \sqrt5b$

$\implies \dfrac{49 + 12\sqrt5}{4 - 49} = a+\sqrt5b$

$\implies \dfrac{49 + 12 \sqrt5}{-45} = a + \sqrt5b$

$\implies \dfrac{-49}{45} - \dfrac{12 \sqrt5}{45} = a + \sqrt5b$

$\boxed{\implies{\boxed{ a = \dfrac{-49}{45} , \: b = \dfrac{-4}{15}}}}$