solutions to an equation question

**finalfantasy** · Sep 19th 2008, 05:01 PM

(x-3)^(1/2) - (x)^(1/2) = -3

How many solutions, if any are in this equation? I can't seem to be able to factor this :S Any suggestions are greatly appreciated!

**o_O** · Sep 19th 2008, 05:18 PM

$\begin{array}{rcl} \sqrt{x-3} - \sqrt{x} & = & - 3 \\ \sqrt{x - 3} & = & \sqrt{x} - 3 \\ x - 3 & = & x - 6\sqrt{x} + 9 \qquad \text{Squared both sides} \\ 6\sqrt{x} & = & 12 \\ & \vdots & \end{array}$

What can you concude?

**Soroban** · Sep 19th 2008, 06:36 PM

Hello, finalfantasy!

$\sqrt{x-3} - \sqrt{x} \;=\; -3$

How many solutions, if any, are in this equation?[

Why are you trying to factor?

We have:

. $\sqrt{x-3} \;=\;\sqrt{x} - 3$

Square both sides:

. . $x - 3 \;=\;x - 6\sqrt{x} + 9$

. . . $6\sqrt{x} \;=\;12$

. . . $\sqrt{x} \;=\;2$

. . . . $x \;=\;4\quad\hdots$ . but this root is extraneous

There are no solutions.

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