Question

- if x3



+ y3



+ z3



= 3(1 + xyz), p = y + z – x, q = z + x – y and r = x + y – z, then what is the value of p3



+ q3



+ r3– 3pqr?

Answer 1

x3+y3+z3=3+3xyz
x3+y3+z3-3xyz=3
p+q+r=x+y+z
so p3+q3+r3-3pqr=x3+y3+z3-3xyz=3

Answer 2

Answer:

Value of p³ + q³ + r³ - 3pqr is 3

Step-by-step explanation:

Given statement :

x³ + y³ + z³ = 3(1 + xyz)

⇒ x³ + y³ + z³ = 3 + 3xyz

⇒ x³ + y³ + z³ - 3xyz = 3

p = y + z - x  , q = z + x - y and r = x + y - z

⇒ p + q + r = (y + z - x) + (z + x - y) + (x + y -z) = y + z - x + z + x - y + x + y -z

                  = x + y + z

So, p³ + q³ + r³ - 3pqr =  x³ + y³ + z³ - 3xyz = 3

Therefore, Value of p³ + q³ + r³ - 3pqr is 3