Question

If the number pis 7 more than
the number g and the sums of
the squares of p and q is 85.
find the difference of cube of
p and a​

Answer 1

Answer:-

Given:-

A number p is 7 more than q.

→ p = q + 7

→ p - q = 7 -- equation (1)

And,

Sum of their squares = 85

→ p² + q² = 85 -- equation (2)

We know that,

(a - b)² = a² + b² - 2ab

Hence,

→ (p - q)² = (p² + q²) - 2pq

Putting the values from equations (1) & (2) we get,

→ (7)² = (85) - 2pq

→ 49 - 85 = - 2 pq

→ - 36/ - 2 = pq

→ pq = 18 -- equation (3)

We know,

a³ - b³ = (a - b) * (a² + b² + ab)

→ p³ - q³ = (p - q) * (p² + q² + pq)

Putting the values from equations (1) , (2) and (3) we get,

→ p³ - q³ = (7) * ( 85 + 18)

→ p³ - q³ = (7) * (103)

→ p³ - q³ = 721

Hence, the difference of cubes of p and q is 721.