Question

find the value of p³-q³ if p-q=10/9 and pq =5/3

Answer 1

as we know the identity

a³-b³=(a-b) (a²+ab+b²)

so

p³-q³=(p-q) (p²+pq+q²)

first we have to find p²+q²

(p-q) ²=p²+q²-2pq


(10/9) ²=p²+q²-2(5/3)

100/81=p²+q²-10/3

p²+q²=100/81+10/3

p²+q²=370/81

now we have values of p²+q², pq, p-q

put values

p³-q³=(p-q) (p²+pq+q²)

=(10/9) (370/81+5/2)

solve further you will get answer

Answer 2

p^3 -q^3 = (p-q)^3 + 3pq(p-q)

= (10/9)^3 + 3(5/3)(10/9)

=1000/27 + 50/9
=1000+150/27
=1150/27
=45.5925 almost
i hope this will help u