SOLUTION: So theres a line A----------- M----------- -B and M is the midpoint AM is x^2-6 BM is x what is AB? Please write out all the steps, thank you.

Algebra ->  Length-and-distance -> SOLUTION: So theres a line A----------- M----------- -B and M is the midpoint AM is x^2-6 BM is x what is AB? Please write out all the steps, thank you.      Log On


   

Question 909293: So theres a line
A------------M-------------B
and M is the midpoint
AM is x^2-6
BM is x
what is AB?
Please write out all the steps, thank you.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
A------------M-------------B
M is the midpoint => AM=BM
if AM+=x%5E2-6
and BM+=x
then x%5E2-6=x ...solve for x
x%5E2-x-6=0 ...write -x as 2x-3x
+x%5E2%2B2x-3x-6+=+0+ ...group
+%28x%5E2%2B2x%29-%283x%2B6%29+=+0+
+x%28x%2B2%29-3%28x%2B2%29+=+0+
+%28x-3%29%28x%2B2%29+=+0+
solutions
if +x-3=+0+ => x=3
if +x%2B2=+0+ => x=-2 since AB is a line and we need the length, we will use only positive solution x=3
now find AM+=x%5E2-6 and BM+=x
BM+=x=> BM+=3
AM+=3%5E2-6 => AM+=3

then AB=AM%2BBM=3%2B3=6