Elimination of Squares

[Ruben]

Hi,

Can anyone help me answer this qiestion?

If I have (2x+3)^2=36 I am not allowed to eliminate the power by square rooting all the equation as I would loose one of the two zeros, right?

In turn I can rise to the 2nd power sqrt(x+y)=9 to remove the sqrt and so get x+y= 3, rightr?

Thanks,

Ruben

[Ruben]

Can anyone help?

[rfernandez]

Hi,

Can anyone help me answer this qiestion?

If I have (2x+3)^2=36 I am not allowed to eliminate the power by square rooting all the equation as I would loose one of the two zeros, right?

In turn I can rise to the 2nd power sqrt(x+y)=9 to remove the sqrt and so get x+y= 3, rightr?

Thanks,

Ruben

To your first question, you may take the square root of both sides, but two equations will result, one with a positive result and the other negative:

(2x + 3)^2 = 36
2x + 3 = 6 OR 2x + 3 = -6
x = 3/2 OR x = -9/2

This technique makes sense because in the original equation, it is stated that (2x+3), when squared, equals 36. Well, that leaves exactly two possibilities for (2x+3): it's either 6 or -6. Set up both of these equations to get to the values of x that make the original equation true.

To your second question, you may square both sides, but in general there's a possibility you'll produce an "extraneous" solution. That doesn't appear to be an issue with this equation, but watch out for it in general.

sqrt(x + y) = 9
x + y = 81

In your original post, by the way, you squared the left side and took the square root of the right side. To keep the equality, you must perform the SAME operation to both sides, as I did above.

[Ruben]

Hey Rey,

Thanks for the answer. This means I should have posted sqrt(x+y)=sqrt 9 I guess!

Best,

Ruben