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h0pe
 one year ago
If \(554_b\) is the base \(b\) representation of the square of the number whose base \(b\) representation is \(24_b,\) then find \(b\).
h0pe
 one year ago
If \(554_b\) is the base \(b\) representation of the square of the number whose base \(b\) representation is \(24_b,\) then find \(b\).

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myininaya
 one year ago
Best ResponseYou've already chosen the best response.2wait so it kind of looks like it is saying this: \[554_b=(24_b) \cdot (24_b)\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2and of course we are to find the b there

h0pe
 one year ago
Best ResponseYou've already chosen the best response.1I think that looks about right

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2\[5 \cdot b^2+ 5 \cdot b+4=(2 \cdot b+4)(2 \cdot b +4)\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2this looks like a quadratic equation

h0pe
 one year ago
Best ResponseYou've already chosen the best response.1so then \((2b+4)(2b+4)\) is \(4b^2+8b+8\) right?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2well not exactly 4(4)=16 and 2b(4)+4(2b)=16b

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2check that middle term and last term you have

h0pe
 one year ago
Best ResponseYou've already chosen the best response.1They are 16s whoops \(4b2+16b+16\)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2right so you have \[5b^2+5b+4=4b^2+16b+16\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2you need to some subtraction on both sides

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2\[\text{ or } b^211b12=0\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2which you can factor the left hand side

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2or you can use the quadratic formula if you really want to but factoring the left hand expression is not too bad

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2you will get one b that makes sense and the other b that makes no sense

h0pe
 one year ago
Best ResponseYou've already chosen the best response.1what do you mean by factoring? sorry it's been a while since I've used that. 0.0

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2like to factor something like x^25x+6 you can look for two numbers that multiply to be 6 and add up to be 5 so 2(3)=6 and 2+(3)=5 so x^25x+6 can be written as (x2)(x3) and if you wanted to solve x^25x+6=0 you can write this first as (x2)(x3)=0 then set both factors equal to zero x2=0 or x3=0 so x=2 or x=3 you can find two numbers that multiply to be 12 and add up to be 11

h0pe
 one year ago
Best ResponseYou've already chosen the best response.1For the case of \(b^2−11b−12=0\) it would be 12 and 1, wouldn't it be? So the equation would be \((b12)(b+1)\) right?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2bingo so you have to solve (b12)(b+1)=0 which means you have either b12=0 or b+1=0 (or both <both will not work in this case and I hope you will see why )

h0pe
 one year ago
Best ResponseYou've already chosen the best response.1The answer has to be \(b=12\), because there aren't negative bases.
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