Question

In a number system with base b,15*22=363 the value of b is

Answer 1

15 = b + 5

22 = 2b + 5

363 = 3b² + 6b + 3

so (b+5) (2b+5) = 3b² + 6b + 3

2b² + 5b + 10b + 25 = 3b² + 6b + 3

3b² - 2b² + 6b - 15b + 3 - 25 = 0

b² - 9b - 22

(b+2)(b-11)

b = -2, 11