Question

If (p+q)=3 then what is the value of (p3 + q3), when it is given that p=1/q?

Answer 1

Formula :

(a+ b)³ =a ³ +b³ +3ab(a + b)

⇒ a³ +b³ = (a+ b)³  - 3ab(a + b)

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Given ( p + q) = 3 and p = 1/q:

p³ + q³ = (p + q)³ -  3pq(p + q)

p³ + q³ = (3)³ -  3(1/q)q(3)

p³ + q³ = 27 -  9

p³ + q³ = 18

Answer: 18

Answer 2

The given solution is of (p+q)=3 find (p^3+q^3) if p=1/q so now equate the solution that is take down the number 3 and then multiply it with pq.  

p^3+q^3=(p+q)^3 – 3pq(p+q),

=> p^3+q^3=(3)^3-3(1/q)q(3),

=> p^3+q^3=27-9,=> p^3+q^3=18.

Thus for the solution (p^3+q^3) is 18 which gets calculated by the fraction of p=1/q.