Öx - 6 + Öx = 6
Isolate the more complicated radical term:
Öx - 6 = 6 - Öx
Square both sides:
(Öx - 6)² = (6 - Öx)²
x - 6 = (6 - Öx)(6 - Öx)
x - 6 = 36 - 6Öx - 6Öx + x
x - 6 = 36 - 12Öx + x
Isolate the radical term on the right
42 = 12Öx
Divide both sides by 6
7 = 2Öx
Square both sides:
7² = (2Öx)²
49 = 4x
= x
You must check all radical equation because sometimes
squaring both sides often introduces extraneous "solutions".
It'll be easier to check if we convert to a decimal 12.25
Öx - 6 + Öx = 6
Ö12.25 - 6 + Ö12.25 = 6
Ö6.25 + Ö12.25 = 6
2.5 + 3.5 = 6
6 = 6
So the solution is or 12.25
Edwin
In the future, use sqrt(*expression*) to indicate square root. Use either sqrt[n](x) or root(x,n) to indicate
The first thing is that you don't want to have two terms with a radical on one side of an equation if you can help it. In this case, add to both sides of the equation:
Square both sides
Rearrange, collect terms, etc.
Multiply both sides by and then reduce the fraction in the RHS.
Square both sides:
John
My calculator said it, I believe it, that settles it
