Question

if p q r are in ap then p^3+r^3-8q^3 is equal to

Answer 1

Answer:

- 6prq

Step-by-step explanation:

Given If p q r are in A.P then p^3 + r^3 - 8 q^3 is equal to

Now p,q and r are in A.P, so common difference will be

(q – p) = (r – q)

So q = p + r / 2

So p + r = 2 q ------------1

Now  

P^3 + r^3 – 8q^3 substituting for q we get

= p^3 + r^3 – 8 (p + r / 2)^3

= p^3 + r^3 – 8 (p + r)^3 / 8

= p^3 + r^3 – (p + r)^3

= p^3 + r^3 – (p^3 + r^3 + 3pr(p + r) )

= p^3 + r^3 – p^3 – r^3 – 3pr(p + r)

= - 3pr(p + r)

= - 3pr (2q) from 1

= - 6 prq

Therefore p^3 + r^3 – 8q^3 = - 6pqr

Answer 2

Answer:

Ur answer is below attached...

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