a)

True or false?

b)

True or false?

Can you please help me understand this.

Printable View

- Jan 31st 2010, 08:31 PMAnemoriSolving equations containing square roots.
a)

True or false?

b)

True or false?

Can you please help me understand this. - Jan 31st 2010, 08:47 PMhalpo
- Jan 31st 2010, 09:07 PMhalpo
Here's B anyway since it's more involved....

Square both sides...

Subtract 36, 7x, and 2 from the right.

Look, we can divide the equation by -6.

Square both sides again...

Distribute the 4.

Subtract 28x and 8 from the right.

This factors to...

So our solutions are 14 and 2. Check them! You will find that 2 is the only solution and thus the statement is true. - Jan 31st 2010, 09:27 PMAnemori
Thank you that was awsome....

- Feb 5th 2010, 01:30 AMAnemori
- Feb 5th 2010, 02:47 AMHallsofIvy
Were those really "true or false" questions? I would interpret "true or false" for an equation involving, say, x, to be asking if it was true for

**all**x- and that's clearly false for both questions.

To solve equations involving , you**square**to get rid of the square roots. After getting to , square again to get which is the same as . Either x= 0 or x- 4= 0 so x= 4.

Since squaring both sides like that can introduce "extraneous roots", you should always check by putting the numbers into the original equation. The original equation was [tex]\sqrt{2x+1}- \sqrt{x}= 1[tex]. With x= 0 that becomes so x= 0 is a solution. With x= 4, it becomes so x= 4 is also a solution.