Question

Find the value of p^3-q^3 if p-q=-7 and pq= -10

Answer 1

-203

Explanation:

We know that by formula

p^3 – q^3 = (p – q) (p^2 + pq + q^2 ) -------(1)

(p-q)^2 = p^2 -2pq +q^2 --------(2)

Solving eq(1)

(-7)^2 = p^2 -2(-10) +q^2

49 = 10 +p^2 + q^2

p^2 + q^2 = 39--------(3)

Given:

p-q = -7

pq = -10

Put all given values and eq(3) in eq(1)

p^3 - q^3 = (-7) (39-10)

p^3 - q^3 = (-7) (29)

p^3 - q^3 = -203