Flag Magical Mathematics[Interesting Approach]> if a,b,c are in A.P., prove that 8b^3-a^3...
question mark

if a,b,c are in A.P., prove that 8b^3-a^3-c^3=3ac(a+c)

MANJU RATHOUR , 7 Years ago
Grade 12th pass
anser 1 Answers
Arun

Last Activity: 7 Years ago

c-b=b-a

2b=a+c

b=(a+c)/2

a^3+c^3-8b^3=a^3+c^3-8 ((a+c)/2)^3

=a^3+c^3 - 8((a^3+3a^2c+3ac^2+c^3)/8)  (since (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3)

=a^3+c^3-a^3-3a^2c-3ac^2-c^3

=-3a^2c-3ac^2

=-3ac(a+c)

 

Or we can say

 

8b³-a³- c³ = 3ac(a+c)

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...