Expert: Lynn Houston - 9/24/2008

Question
Hi,
I have a equation for which I need to find the real solutions
Q:- The equation square root (under this square root is x-3) - square root (under this square root is x) = -3

Sorry I can not find the square root notation anywhere else than my calculator. Since it is a multiple choice question
All the chocies are
a) has no real solution
b)has exactly one real solution
c) has exactly two real solutions
d) has exactly three differtn real solutions
e) has nove of the above properties.

This question is a diagnostic question for the first year precalc quiz and I have been away from math for 2 years sicne i had a year off my high school and now have trouble understanding basic math concepts.

Plz help
Thanks in advance.

Answer
B

If you want to know how to solve it.  You sq both sides of the eq, which gives leaves you with x-3 -2sq rt (x^2-3x) + x = 9.  Move all but the sq rt to the other side of the eq and then sq both sides again.  So, 2sq rt(x^2-3x) = -2x +12, sq both sides, you get 4(x^2-3x) = 4x^2 + 48x + 144.  Distribute the 4 and combine like terms, gives you -60x = 144.  Divide both sides by -60 and you get exactly one real solution - x = -12/5