Can you Solve Cambridge University Admission Interview Question ?

[@ChavoMysterio]

Ferrari Method?

[@9허공]

Another approach without calculator
let a = √(16 - x) => a^2 = 16 - x ---(1) a = 16 - x^2 ---(2)
(1) - (2) a^2 - a = x^2 - x => x^2 - a^2 - x + a = (x + a)(x - a) - (x - a) = (x - a)(x + a - 1) = 0
( case x - a = 0 )
x^2 = 16 - x => x^2 + x - 16 = 0 => x = (-1±√65)/2
since 8 < √65 < 9 => -5 < (-1-√65)/2 < -4.5 , 3.5 < (-1+√65)/2 < 4 => x = (-1+√65)/2
( case x + a - 1 = 0 )
x + (16 - x^2) - 1 = 0 => x^2 - x - 15 = 0 => x = (1±√61)/2
since 7 < √61 < 8 => 4 < (1+√61)/2 < 4.5, -3.5 < (1-√61)/2 < -3 => x = (1-√61)/2
Answer x = { (-1+√65)/2, (1-√61)/2 }