Question

find the value of p³-q³, if p-q=10 and pq=15.​

Answer 1

Answer:

p³-q³= 1450

Step-by-step explanation:

p-q = 10 , pq = 15 , find p³-q³

p-q = 10

cube on both sides,

(p-q)³ = (10)³

p³-q³-3pq(p-q) = 1000

< formula of p³-q³ = p³- q³-3pq(p-q) >

p³-q³=1000 + 3pq(p-q)

p³-q³= 1000 + 3 (15) (10)

<substitute value of pq and p-q>

= 1000 + 45 (10)

= 1000 + 450

= 1450

hope it helps :)

Answer 2

Required Answer:-

We need to find p³ - q³ by the formula:

$\boxed{ \rm{ \red{ {p}^{3} - {q}^{3} = (p - q)( {p}^{2} + pq + {q}^{2})}}}$

We have,

• p - q = 10 ..(1)
• pq = 15 ..(2)

Squaring the first equation,

⇒ (p - q)² = 100

⇒ p² - 2pq + q² = 100

Add 3pq on both sides,

⇒ p² - 2pq + q² + 3pq = 100 + 3pq

Put the value of pq on the right side,

⇒ p² + pq + q² = 100 + 3(15)

⇒ p² + pq + q² = 145

Then,

⇒ p³ - q³ = 10 × 145

⇒ p³ - q³ = 1450

The final answer:-

$= \large{ \boxed{ \boxed{ \rm{1450}}}}$