Question

Root5 /2 root5 -1

can be written in the form
a+rootb /c
where a, b and c are integers.
Find the values of a, b and c when the resulting fraction
is written in its simplest form.

Answer 1

10, 5, 19

Explanation:

Recall that

`{a}^(2) - {b}^(2) = (a + b)(a - b)`

So we can multiply the fraction by

`(2 √(5) + 1 )/(2 √(5) + 1 )`

And get

`( √(5) )/(2 √(5) - 1) * (2 √(5) + 1 )/(2 √(5) + 1 ) = (10 + √(5) )/(20 - 1) = (10 + √(5) )/(19)`