Question

If (p+q+r=5) and pq+qr+rp = 10, then the value of p³+q³+r³-3pqr will be ?

Answer 1

Answer:

        -25

Step-by-step explanation:

Use:

   (p + q + r)³  =  p³ + q³ + r³ - 3pqr + 3(p + q + r)(pq + qr + rp)

Rearranged, this gives:

   p³ + q³ + r³ - 3pqr  =  (p + q + r)³ - 3(p + q + r)(pq + qr + rp).

Substituting the given values for p+q+r and pq+qr+rp gives:

   p³ + q³ + r³ - 3pqr  =  5³ - 3×5×10  =  125 - 150 = -25

Answer 2

Formula Used :

$\bold{a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-(ab+bc+ac))}$

Explanation :

Here ,

p + q + r = 5 ... (1)

pq + qr + rp = 10 ... (2)

Now  (1)  on both sides , we get ,

⇒ ( p + q + r )² = 5²

⇒ p² + q² + r² + 2pq + 2qr + 2rp = 25

⇒ p² + q² + r² + 2 ( pq + qr + rp ) = 25

⇒ p² + q² + r² + 2 (10) = 25 [ From (2) ]

⇒ p² + q² + r² = 25 - 20

⇒ p² + q² + r² = 5 ... (3)

Now our required ,

⇒ p³ + q³ + r³ - 3pqr

⇒ ( p + q + r ) ( p² + q² + r² - ( pq + qr + rp ))

⇒ ( 5 ) ( 5 - 10 ) [ From (1) , (2) , (3) ]

⇒ 5 ( -5 )

⇒ - 25

So the value of p³+q³+r³-3pqr is - 25 .