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)+(k26k+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

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