If 554b is the base b representation of the square of the number whose base b representation is 24b then find b.
I've had tons of trouble with this problem. I am practicing different bases and would appreciate help!
+23251 24b = 2·b + 4
(24b)2 = (2·b + 4)·(2·b + 4) = 4b2 + 16b + 16
554b = 5·b2 + 5·b + 4 = 5b2 + 5b + 4
Since these are equal: 5b2 + 5b + 4 = 4b2 + 16b + 16
---> b2 - 11b - 12 = 0
---> (b - 12)(b + 1) = 0
---> Either b = 12 or b = -1
---> Since the base is positive, b = 12
If you want to check this: 2412 = 2·12 + 4 = 26 (base ten)
---> (2412)2 = (26)2 = 784 (base ten)
Also: 55412 = 5·(12)2 + 5·(12) + 4 = 784 (base ten) <--- They are equal!
It is not clear to me what you are trying to do. If you are trying to convert a number from one base to another, then there is a procedure to do it: Example: convert 100 from base 10 to base, 2, base 4 and base 5. Then you get these answers:1100100_2, 1210_4, 400_5........etc.
+23251 24b = 2·b + 4
(24b)2 = (2·b + 4)·(2·b + 4) = 4b2 + 16b + 16
554b = 5·b2 + 5·b + 4 = 5b2 + 5b + 4
Since these are equal: 5b2 + 5b + 4 = 4b2 + 16b + 16
---> b2 - 11b - 12 = 0
---> (b - 12)(b + 1) = 0
---> Either b = 12 or b = -1
---> Since the base is positive, b = 12
If you want to check this: 2412 = 2·12 + 4 = 26 (base ten)
---> (2412)2 = (26)2 = 784 (base ten)
Also: 55412 = 5·(12)2 + 5·(12) + 4 = 784 (base ten) <--- They are equal!
