Question

The integers 220, 251, and 304 represent three consecutive perfect squares in base "b". Determine the value of "b".

Answer 1

you'll have to solve a system of equations. If you let b be the base, and x^2, (x+1)^2, and (x+2)^2 be the consecutive squares, you get the system:\[2b^2+2b+0=x^2\]\[2b^2+5b+1=(x+1)^2\]\[3b^2+0b+4=(x+2)^2\]Your job is to find out what b is. Note, since the digit 5 appears in one of the numbers, the base must be bigger than 5, so you can start with 6 if you are going to guess and check.

Answer 2

If you think b = 6, then check to see if:\[2(6)^2+2(6)+0\]is a perfect square. If it isnt, then move on to 7.

If you dont feel like guess n' check, then you have to solve the system by whatever means (substitution, elimination, etc).

Answer 3

@joemath314159
i got it i think..
im pretty sure its 8 cuz when i plug it in i get 144

Answer 4

8 is correct :) note that when you plug in 8 to the second and third equations, you get 169 and 196, so it follows what the problem said about the consecutive squares:

12^2= 144
13^2 = 169
14^2 = 196.

Answer 5

@joemath314159
ohhh i didnt even think about plugging that in :O
thank you so much :D