Question

the value of  p3+8q3 if p+2q=8 and pq=6 is

                  

Answer 1

p+2q=8 
Taking cube both the sides.
$p^{3} +8 q^{3} +3pq(p+q)=512$
Simply putting the formula⇒$(a+B)^{3} =a^3+b^3+3ab(a+b)$
then putting value pq=6 in the above equation. we get.
$p^3+8q^3+18(p+q)=512$
Now take 18(p+q) in the right
$p^3+8q^3=512-18(p+q)$
Now take the equation p+2q=8
⇒p+q+q=8
⇒p+q=8-q
now taking the value of p+q and putting in the above generated equation we get
$p^3+8q^3=512-144(q)$

Answer 2

p

3

+8q

3

=512−144(q)...............