In base b, \(24_b^2 = 521_b\) Find base b.
521b = 5·b2 + 2·b + 1
24b = 2·b + 4
(24b)2 = (2b + 4)2 = 4b2 + 16b + 16
(24b)2 = 521b ---> 4b2 + 16b + 16 = 5b2 + 2b + 1
0 = b2 - 14b - 15
0 = (b - 15)(b + 1) ---> b = 15
