Question

sum p of the square of q and the cube of r​

Answer 1

Step-by-step explanation:

Denote the roots by a,b,c; then

a+b+c=p,bc+ca+ab=q.

Now a

2

+b

2

+c

2

=(a+b+c)

2

−2(bc+ca+ab)

=p

2

−2q.

Again, substitute a,b,c for x in the given equation and add; thus

a

3

+b

3

+c

3

−p(a

2

+b

2

+c

2

)+q(a+b+c)−3r=0;

∴a

3

+b

3

+c

3

=p(p

2

−2q)−pq+3r

=p

3

−3pq+3r.