Arithmetic mean - parabola

Find the value of k so that k2 + 2k – 3 is the arithmetic mean between k2 + 4k + 5 and k2 – 6k + 10.

Correct answer:

k =  3.5

Step-by-step explanation:

m= 2a+b   k2+2k3 = ((k2 + 4k +5) + (k2  6k + 10) )/2  3k10.5=0  3 k10.5=0  3k=10.5  k=310.5=3.5=27=321  k=27=3.5   Verifying Solution:   a=k2+4 k+5=3.52+4 3.5+5=4125=3141=31.25 b=k26 k+10=3.526 3.5+10=45=141=1.25 M=k2+2 k3=3.52+2 3.53=465=1641=16.25 m=2a+b=24125+45=465=1641=16.25  M=m

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Looking for help with calculating arithmetic mean?
Looking for a statistical calculator?
Are you looking for help with calculating roots of a quadratic equation?
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?
The Pythagorean theorem is the base for the right triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: