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+2k−3 = ((k2 + 4k +5) + (k2 − 6k + 10) )/2  3k−10.5=0  3⋅ k−10.5=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=k2−6⋅ k+10=3.52−6⋅ 3.5+10=45​=141​=1.25 M=k2+2⋅ k−3=3.52+2⋅ 3.5−3=465​=1641​=16.25 m=2a+b​=24125​+45​​=465​=1641​=16.25  M=m

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