How do you solve x - 3 = sqrt(x - 1) and find any extraneous solutions?
1 Answer
Mar 12, 2017
Explanation:
color(blue)"square both sides"
(x-3)^2=(sqrt(x-1))^2
rArrx^2-6x+9=x-1 Equate the quadratic to zero
rArrx^2-7x+10=0 Factorising the quadratic gives.
(x-2)(x-5)=0
rArrx=5" or "x=2
color(blue)"As a check" Substitute these values into the equation and if the left side equals the right side then they are the solutions.
• x=5to5-3=sqrt(5-1)to2=2rArr" a solution"
• x=2to2-3=sqrt1to-1=1rArr" not a solution"
rArrx=5" is the solution, but "x=2" is extraneous"
