How do you solve #3sqrtk+1=6# and find any extraneous solutions?

1 Answer
Aug 26, 2016

Answer:

#25/9#

Explanation:

We require to isolate the square root term.

subtract 1 from both sides

#rArr3sqrtk+cancel(1)-cancel(1)=6-1rArr3sqrtk=5#

divide both sides by 3

#rArr(cancel(3)^1 sqrtk)/cancel(3)^1=5/3rArrsqrtk=5/3#

#color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtkxxsqrtk=(sqrtk)^2=k)color(white)(a/a)|)))#

Squaring both sides to obtain k

#rArr(sqrtk)^2=(5/3)^2#

#rArrk=5^2/3^2=25/9#

There are no extraneous solutions.