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If:

$$a = \sqrt{ b^2 - b }$$

The problem I have is that for values of:

$0 < b < 1$

the result of:

$b^2 - b$

Is a negative number which gives rise to an error on Excel and my calculator.

I understand that negative numbers don't have square roots (I read it on Wikipedia at least), so how do I solve this for values of $b$ less than 1?

Thanks! :)

  • 0
    There's a reasonable question here as to why you think there *is* a solution. If $a = \sqrt{b^2 - b}$ then $a^2 = b^2 - b$, so when $b^2 - b$ is negative you are really saying "I know that the square of a number is always positive but what if it isn't?". As pointed out in answers, there are contexts where in fact the square of a number is not positive, but I think you should also just accept that sometimes an equation can have no solutions, or many solutions, and you can't just go ahead and solve for whatever you want.2012-05-17
  • 0
    Just to note that if you want to work with such things in Excel, you can use an IF(condition,value if true,value if false) function to bypass the error.2012-05-17
  • 0
    Good point Mark, I'll do that!2012-05-18

3 Answers 3