SOLUTION: I need to resolve x, AB, BC and AC, where A, B and C are points on a line. A is leftmost, C is rightmost, and B is somewhere in between. AB = 2x+1 BC = x-2 AC = sqrt (x^2 + 2

Question 156834: I need to resolve x, AB, BC and AC, where A, B and C are points on a line. A is leftmost, C is rightmost, and B is somewhere in between.
AB = 2x+1
BC = x-2
AC = sqrt (x^2 + 25x + 5)
Was able to write, 2x+1+x-2 = sqrt (x^2+25x+5), which reduces to 3x-1 = sqrt (x^2 + 25x + 5).
I don't know how to eliminate the square root, especially when there is an exponential along with it.
Please help.
Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll start where you left off

Start with the given equation

Square both sides. This will eliminate the square root.

FOIL the left side

Subtract from both sides. Subtract from both sides. Subtract from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, if you plug in back into the original equation, you'll find that the equation won't be true. Also, since distance is ALWAYS positive, this means that will not work (since if you plug it into any expression the result is negative)

So the only answer is

Now plug in into AB,BC, and AC:

AB =
BC =
AC =

So the three lengths are , , and

Check:

Remember, the segment addition postulate is AB+BC=AC (ie the lengths of the pieces of AC should add to the length of AC)

AB+BC=AC ... Start with the given equation

9+2=11 ...Plug in AB=9, BC=2, and AC=11

11=11 ... Add. Since this equation is true, this verifies the answer.
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