1.18: Past-paper question 1

4PM1/2/June/2023 — Question 1 · 5 marks

Given that a+253−5=11+b52\displaystyle \frac{a + 2\sqrt{5}}{3 - \sqrt{5}} = \frac{11 + b\sqrt{5}}{2} where a\displaystyle a is an integer and b\displaystyle b is prime,
find the value of a\displaystyle a and the value of b\displaystyle b
Show your working clearly.
(5)