Question

How do you solve `w = sqrt[7w]` and find any extraneous solutions?

Answer 1

`w=0 and w=7`

However we have a square root so for the solution `in RRcolor(white)("d"); w>=0`

Explanation:

Given: `w=sqrt(7w)`

Square both sides

`w^2=7w`

Subtract `7w` from both sides

`w^2-7w+0=0`

And we have our quadratic!

compare to `aw^2+bw+c=0 color(white)("ddd") ->color(white)("ddd") w=(-b+-sqrt(b^2-4ac))/(2a)`

`w=(7+-sqrt((-7)^2-4(1)(0)))/(2(1))`

`w=7/2+-7/2`

`w=0 and w=7`