Question

(i) х³ - у³ - z³ - 3xyz​

Answer 1

Answer:

x3 + y3 + z3 - 3xyz

= (x + y + z)(x2 + y2 + z2 - xy - yz - zx)

If x + y + z = 0, then x3 + y3 + z3 = 3xyz

x = 7, y = -10 and z = 3

x + y + z = 7 - 10 + 3 = 0

73 - 103 + 33 = 3(7)(-10)(3) = -630

(ii) 1 + (1/8) - (27/8)

hope it's useful.

thank you so much.

Answer 2

Given,

x3 + y3 + z3 - 3xyz

= (x + y + x) * (x2 + y2 + z2 - xy - yz - zx)

= (1/2) * (x + y + x) * (2x2 + 2y2 + 2z2 - 2xy - 2yz - 2zx)

= (1/2) * (x + y + x) * [(x - y)2 + (y - z)2 + (z - x)2 ]

Hence,

x3 + y3 + z3 - 3xyz = (1/2) * (x + y + x) * [(x - y)2 + (y - z)2 + (z - x)2 ]