Question

x is an integer and 9 < x2 < 99. What is the maximum value of x minus the minimum value of x?

Answer 1

\[9<x^2<99 \]

Answer 2

implies \[-3<x<\sqrt{99}\]

Answer 3

so max -min =
\[\sqrt{99}-(-3)=\sqrt{99}+3=3(1+\sqrt{11})\]