• Nov 4th 2006, 08:44 PM
shenton
How to solve this:

-3 √(6x+5) = -9

Do we use conjugate of -3 √(6x+5)? If so, what is the conjugate of -3 √(6x+5)?

example: The conjugate of (x + √y) is (x - √y).

I don't think the conjugate of -3 √(6x+5) is -3 √(6x-5) since the above example has 2 terms, that is x and √y while -3 √(6x+5) is only 1 term.

Thanks.
• Nov 4th 2006, 11:58 PM
CaptainBlack
Quote:

Originally Posted by shenton
How to solve this:

-3 √(6x+5) = -9

You start by squaring to get:

$\displaystyle \left[ -3 \sqrt{6x+5}\right]^2 = (-9)^2$

which simplifies to:

$\displaystyle 9 (6x+5) = 9^2$

further simplification gives:

$\displaystyle 6x = 4$

which si,plifies further to $\displaystyle x=2/3$.

Now as we squared the original equation we need to check that
any solution we subsequently find satisfies the original equation
as squaring can introduce spurious solutions. But in this case there
is no problem and $\displaystyle x=2/3$ is the solution.

RonL
• Nov 5th 2006, 10:50 AM
shenton
Thanks for the help!