Question

What is the value of p³(q-r)³ +q³(r-p)³+r³(p-q)³ ?( No useless answers please)

Answer 1

Step-by-step explanation:

Given:-

p³(q-r)³ +q³(r-p)³+r³(p-q)³

To find:-

What is the value of p³(q-r)³ +q³(r-p)³+r³(p-q)³ ?

Solution:-

Given expression is p³(q-r)³ +q³(r-p)³+r³(p-q)³

=>[p(q-r)]³+[q(r-p)]³+[r(p-q)]³

=>(pq-pr)³+(qr-pq)³+(pr-qr)³

This is in the form of a³+b³+c³

Here, a=pq-pr

b=qr-pq

c=pr-qr

and a+b+c=0

=>pq-pr+qr-pq+pr-qr

=>(pq-pq)+(pr-pr)+(qr-qr)

=>0

We know that

If a+b+c=0 then a³+b³+c³=3abc

(pq-pr)³+(qr-pq)³+(pr-qr)³

=>3(pq-pr)(qr-pq)(pr-qr)

=>3pqr(q-r)(r-p)(p-q)

Answer:-

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

Used formula:-

• If a+b+c=0 then a³+b³+c³=3abc

Answer 2

3pqr(p - q)(q - r)(r - p)

Step-by-step explanation:

Given Equation is p³(q - r)³ + q³(r - p)³ + r³(p - q)³

⇒ [p(q - r)]³ + [q(r - p)]³ + [r(p - q)]³

Let a = p(q - r), b = q(r - p), c = r(p - q)

∴ a + b + c = p(q - r) + q(r - p) + r(p - q)

= pq - pr + qr - qp + rp - rq

= 0

We know that when a + b + c = 0, then a³ + b³ + c³ = 3abc

⇒ 3(pq - qr)(qr - qp)(rp - rq)

I hope it will be help you