1. ## Factoring Trouble

All I need to know is what number, when squared, equals 890, and when doubled, equals 60. No, it's not 30. Any ideas?
Perhaps there's no solution. IDK.

2. Originally Posted by hgraff
All I need to know is what number, when squared, equals 890, and when doubled, equals 60. No, it's not 30. Any ideas?
Perhaps there's no solution. IDK.
There is no such number

$2x = 60 \implies \frac{1}{2} * 2x = \frac{1}{2} * 60 \implies x = 30 \implies x^2 = 900 \ne 890.$

3. ## Base -3/2

Originally Posted by hgraff
All I need to know is what number, when squared, equals 890, and when doubled, equals 60. No, it's not 30. Any ideas?
Perhaps there's no solution. IDK.
Yes it is 30,
if all numbers are base -3/2

4. Hello, Bob Brown!

Very imaginative!

Originally Posted by Bob Brown MSEE
Yes it is 30, if all numbers are base -3/2

Let $b$ = base, $bx+y$ = two-digit number.

We have: .$\begin{Bmatrix}(bx+y)^2 \;=\; 8b^2+9b & [1] \\ 2(bx+y) \;=\; 6b & [2] \end{Bmatrix}$

From [2]: .$y \:=\:3b-bx$

Substitute into [1]: .$[bx + (3b-bx)]^2 \:=\:8b^2 + 9b$

. . . $(3b)^2 \:=\:8b^2+9b \quad\Rightarrow\quad 9b^2 \:=\:8b^2 + 9b$

. . . $b^2 - 9b \:=\:0 \quad\Rightarrow\quad b(b-9) \:=\:0$

. . . $\color{red}{\rlap{/////}}{b = 0},\;b = 9$

We are dealing with base-nine.
. . And it turns out that $x = 3,\;y = 0.$

Check:

. . $\begin{Bmatrix}(30_9)^2 \;=\;8\color{purple}{9}0_9 & \Rightarrow & 27^2 \:=\:729 & \checkmark \\ 2(30_9) \;=\;60_9 & \Rightarrow & 2(27) \:=\:54 & \checkmark \end{Bmatrix}$

Unfortunately, there is no "9" in base-nine . . . *sigh*

5. So it is just possible that Bob Brown was right all along?

6. ## Hmmmmmmmm

Originally Posted by HallsofIvy
So it is just possible that Bob Brown was right all along?
possible

7. Originally Posted by Bob Brown MSEE
possible
Instead of "possible," it is definite.

http://en.wikipedia.org/wiki/Negative_base

State it with conviction.

As a tangential example,

one would state with conviction that $2x^2 - x + 3 < 0$

(or similar expression) would not be presented as, say,

2xx - x + 3 < 0.

--------------------------------------------

Edit: "Definitively missing the joke."

Or I "got the joke" and deliberately was dismissive of it.

8. Originally Posted by lookagain
Instead of "possible," it is definite.
Definitively missing the joke.

Question

Originally Posted by HallsofIvy
So it is just possible that Bob Brown was right all along?

Originally Posted by Bob Brown MSEE
possible

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