A tricky Entrance Question from Cambridge University Interview

[@RealQinnMalloryu4]

48/{104+8}=48/112 6^8^/10^12 6^2^3/10^3^4 3^2^1^1^1/2^5^3^4 1^1/1^1^3^2^2 /1^13^1^2 /32 (x ➖ 3x+2).

[@key_board_x]

6/(√13 + 1) = 6.(√13 - 1)/[(√13 + 1).(√13 - 1)]
6/(√13 + 1) = 6.(√13 - 1)/[13 - 1]
6/(√13 + 1) = 6.(√13 - 1)/12
6/(√13 + 1) = (√13 - 1)/2
[6/(√13 + 1)]² = [(√13 - 1)/2]²
[6/(√13 + 1)]² = (√13 - 1)²/4
[6/(√13 + 1)]² = (13 - 2√13 + 1)/4
[6/(√13 + 1)]² = (14 - 2√13)/4
[6/(√13 + 1)]² = (7 - √13)/2
[6/(√13 + 1)]⁴ = { [6/(√13 + 1)]² }²
[6/(√13 + 1)]⁴ = { (7 - √13)/2 }²
[6/(√13 + 1)]⁴ = (7 - √13)²/4
[6/(√13 + 1)]⁴ = (49 - 14√13 + 13)/4
[6/(√13 + 1)]⁴ = (62 - 14√13)/4
[6/(√13 + 1)]⁴ = (31 - 7√13)/2
[6/(√13 + 1)]⁸ = { [6/(√13 + 1)]⁴ }²
[6/(√13 + 1)]⁸ = { (31 - 7√13)/2 }²
[6/(√13 + 1)]⁸ = (31 - 7√13)²/4
[6/(√13 + 1)]⁸ = (961 - 434√13 + 637)/4
[6/(√13 + 1)]⁸ = (1598 - 434√13)/4
[6/(√13 + 1)]⁸ = (799 - 217√13)/2