Question

If p+q+r=0 then show that p3+q3+r3=3pqr

Answer 1

Answer:

p + q + r = 0

we know that,

p³+q³+r³- 3pqr =(p+q+r)(p²+q²+r²-pq-qr-rp)

=> p³+q³+r³- 3pqr = 0 × (p²+q²+r²-pq-qr-rp)

=> p³+q³+r³- 3pqr = 0

=> p³+q³+r³ = 3pqr

Proved

Answer 2

Answer:

the explaination is down there

Step-by-step explanation:

there is an identity ,

p^3 + q^3 + r^3 - 3pqr = (p+q+r)(p^2 +q^2 + r^2-pq-rp-qr)

here we know that

p+q+r = 0

hence

p^3 + q^3 + r^3 - 3pqr = (0)(p^2 +q^2 + r^2-pq-rp-qr)

and anything multiplied by zero is zero

so,

p^3 + q^3 + r^3 - 3pqr = 0

p^3 + q^3 + r^3 = 3pqr

prooved.............