Alternative procedure that takes you nowhere

[errequeerre]

Hello,

I was given these problem to solve:

I could not find a satisfactory solution and I checked the key, which offered me the following steps:
(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

Solution:

I do understand the procedure, but I followed what I think to be an alternative procedure and it took me nowhere. I'd like to know what is wrong with my alternative procedure.
My solution starts being different from step (6):
(6)

(7a)

(8a)

(9a)

which gives two possitibilities, either:
(10a)

or
(11a)

The problem here is that I could not factorize either

or

My assumption, which perhaps is wrong, is that my alternative procedure is correct, but that the impossibility to factorize indicates that I should take the path provided by the solution in the manual. Is that right?

Thanks for your help

 

[MarkFL]

In your alternate method, you make the error of stating:

\(\displaystyle \left(\pm\sqrt{8} \right)^2=\pm8\)

What you want is simply:

\(\displaystyle \left(\pm\sqrt{8} \right)^2=8\)

Squaring both positives and negatives gives a positive result (for real values).

Unless you have been taught the quadratic formula, completing the square is the best route (as your textbook used) since the roots are irrational.

 

[errequeerre]

Thanks, Mark

 

[lookagain]

Hello,

I was given these problem to solve:

I could not find a satisfactory solution and I checked the key, which offered me the following steps:




(1)

(2)

(3)

(4)

(5)

(6)

(7)

\(\displaystyle \ \ \ \ \ \ \) <------ Leave out this step, because the flow of steps is accomplished from step (6) directly to step (8).


(8)

(9)

(10)

(11)

Solution:

.