Question

find the rational number A and B such that 2 minus root 5 by 2 + root 5 is equal to a root 5 + b​

Answer 1

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

multiply the fraction by its denominator's conjugate.

$\frac{(2 - \sqrt{5} )(2 - \sqrt{5}) }{(2 + \sqrt{5} )(2 - \sqrt{5} )} = a + b \sqrt{5} \\ \frac{4 + 5 - 4 \sqrt{5} }{4 - 5} = a + b \sqrt{5} \\ \frac{9 - 4 \sqrt{5} }{1} = a + b \sqrt{5} \\ 9 + ( - 4) \sqrt{5} = a + b \sqrt{5}$

On comparing the LHS, we get

a = 9

b = -4

Answer 2

Answer:

Hope it helps u........