Question 819682
let number of doors be x

2x is a perfect square

doors increased by 2
meaning x+2

{{{(x-2) = sqrt(2x)+10}}}


{{{x-2-10= sqrt(2x)}}}

{{{x-12=sqrt(2x)}}}

square both sides

{{{(x-12)^2= 2x}}}

{{{x^2-24x+144=2x}}}

{{{x^2-26x+144=0}}}

{{{x^2-18x-8x+144=0}}}

x(x-18)-8(x-18)=0

(x-18)(x-8)=0

x=18 OR 8

8 not possible

18 doors