SOLUTION: How many solutions are there to tile equation t^2 = |3t – 2|?

Algebra ->  Equations -> SOLUTION: How many solutions are there to tile equation t^2 = |3t – 2|?      Log On


   

Question 1081800: How many solutions are there to tile equation t^2 = |3t – 2|?
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
3t-2 positive or zero
--------------------

t%5E2=3t-2
t%5E2-3t%2B2=0
%28t-1%29%28t-2%29=0
Two solutions here



3t-2 negative
--------------------

t%5E2=-3t%2B2
t%5E2%2B3t-2=0
t=%28-3%2B-+sqrt%289%2B4%2A2%29%29%2F2
t=%28-3%2B-+sqrt%2815%29%29%2F2
Two DIFFERENT solutions in this case

-----------------
FOUR solutions
-----------------

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
t%5E2+=+abs%283t-2%29 it is same as
t%5E2+=+sqrt%28abs%283t-2%29%5E2%29
so, we have:
t%5E2+=+3t+-2 or t%5E2+=+-%283t-+2%29
if t%5E2+=+3t+-2, we have
t%5E2+-3t+%2B+2=0......factor completely
t%5E2+-t+-2t%2B+2=0
%28t%5E2+-t+%29-%282t-+2%29=0
t%28t+-1+%29-2%28t-+1%29=0
%28t-2%29%28t-+1%29=0
solutions: t=2+and+t=1
and
if +t%5E2+=+-%283t-2%29, we have
+t%5E2+%2B%283t-+2%29=0
+t%5E2+%2B3t+-2=0.........cannot be factor completely,souse quadratic formula
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-2%29+%29%29%2F%282%2A1%29+
t+=+%28-3+%2B-+sqrt%28+9%2B8+%29%29%2F2+
t+=+%28-3+%2B-+sqrt%28+17+%29%29%2F2+
exact solutions:
t+=+%28-3+%2B+sqrt%28+17+%29%29%2F2+
t+=+%28-3+-+sqrt%28+17+%29%29%2F2+
approximate solutions:
t+=+0.56+
t+=+-3.56+
so, you have four solutions all together:
t=2+
+t=1

t+=+%28-3+%2B+sqrt%28+17+%29%29%2F2+ (or t+=+0.56+)
t+=+%28-3+-+sqrt%28+17+%29%29%2F2+ (or t+=+-3.56+)