Question

GUYS NEED HELP VERY URGENTTT

Answer 1

• This is the answer by rationalisation.

Answer 2

Given:

$\dfrac{3 - \sqrt{5} }{3 + 2\sqrt{5} } = a\sqrt{5} - b$

To Find:

The value of a and b

Solution:

$\dfrac{3 - \sqrt{5} }{3 + 2\sqrt{5} } = a\sqrt{5} - b$

LHS:

$\dfrac{3 - \sqrt{5} }{3 + 2\sqrt{5} }$

$= \dfrac{(3 - \sqrt{5})(3 - 2\sqrt{5})}{(3 + 2\sqrt{5})(3 - 2\sqrt{5})}$

$= \dfrac{9 - 6\sqrt{5} - 3\sqrt{5} + 10 }{(3)^2 - (2\sqrt{5})^2 }$

$= \dfrac{19 - 9\sqrt{5} }{9 - 20}$

$= \dfrac{19 - 9\sqrt{5} }{-13}$

$= - \dfrac{19}{13} + \dfrac{9\sqrt{5}}{13}$

$= \dfrac{9}{13}\sqrt{5} - \dfrac{19}{13}$

Comparing LHS and RHS:

$\dfrac{3 - \sqrt{5} }{3 + 2\sqrt{5} } = a\sqrt{5} - b$

$\dfrac{9}{13}\sqrt{5} - \dfrac{19}{13} = a\sqrt{5} - b$

Find the value of a and b:

$a = \dfrac{9}{13}$

$b = \dfrac{19}{13}$

Answer: a = 9/13 and b = 19/13