when f(x) equals g(x)

Question

f(x)= sqaure root of x-8. g(x)=12-x.

What are the values when f(x)=g(x).

Answer 1

sqr(x-8) = 12-x

square both sides to get

x-8 = 144 -24x + x^2

x^2 -25x + 152 = 0

x = 25/2 + or - (1/2)sqr(625-608) = 12.5 + .5(sqr17) = 12.5 + or - 2.06 = about 14.6 or 10.4

check the answers by substituting back into the original equation

sqr(14.6-8) = sqr6.6 = 12-14.6 =-2.6

this would work except the original equation really just involves the positive square root of x-8 and not the negative square root. By multiplying by a variable, we introduced an extraneous solution which is not in the original equation

sqr(10.4-8) = sqr2.4 = 12-10.4 = 1.6

x=about 10.4 rounded off to one decimal is the only solution.