Expert: Ahmed Salami - 11/3/2011

Question
y=sqrt(abs(x)) and y=(x+5)/6. If I solved this problem for intersecting point through squaring on both sides, I got x=-36,-1,4,9. But x=-36 is not a solution. Then why I'm getting -36 as an answer? Please help.....!

Answer
Hi Shameem,
By squaring both sides you get
abs(x) = (x+5)²/36
You need to realise here that;
abs(x) = x for x > 0
and abs(x) = -x for x < 0
You therefore solve the equations;
x = (x+5)²/36    (remembering that only solutions of x > 0 would be valid here)
and
-x = (x+5)²/36   (also only x < 0 solutions would be valid)
Therefore, the solutions are
x = 1 , 25
and
x = -0.55 , -45.45

It would've been better if you showed me your steps so i could actually see where its gone wrong because -36 isnt the only incorrect solution you had as it turns out.

Regards