Final answer:
To find the value of x in the equation XYZ are collinear, we can set up an equation using the lengths of XY, YZ, and XZ. Simplifying, we get a quadratic equation that can be solved to find two possible values of x: -4 or 2.
Step-by-step explanation:
To find the value of x in the equation XYZ are collinear, we can use the fact that collinear points lie on the same line. From the given information, we have XY = x^2 + 3, YZ = 4 + 2x, and XZ = 15. Since X, Y, and Z are collinear, the sum of the lengths XY and YZ should be equal to XZ. Therefore, we can set up an equation: (x^2 + 3) + (4 + 2x) = 15.
Simplifying the equation, we get x^2 + 2x + 7 = 15. Rearranging the terms, we have x^2 + 2x - 8 = 0. To solve this quadratic equation, we can either factor it or use the quadratic formula. Factoring, we get (x+4)(x-2) = 0, which gives us two possible solutions: x = -4 or x = 2.
Therefore, the value of x can be either -4 or 2 in the equation XYZ are collinear.