Question

If p+1/p= 9, find the value of p³+1/p³

Answer 1

the answer is (9)cube  or 729

Answer 2

p+1/p=9
Squaring on both sides we get,
p²+1/p²+2p×1/p=81

p²+1/p²+2=81

p²+1/p²=79
Now let p³+1/p³ be x
p³+1/p³=x

(p+1/p)(p²-p(1/p)+1/p²)=x

9(79-1)=x

9(78)=x

x=702

Hence p³+1/p³=702