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

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Answer 1 · 2018-04-20T20:46:30

#w=0 and w=7#

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

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#

Tony B