Question

If x+y+z=5 and xy+yz+zx=10 then x^3 + y^3 + z^3 - 3xyz = ?

Answer 1

Answer:

Step-by-step explanation:

Answer.

Given x + y + z = 8 and xy + yz + zx = 20

Consider, x + y + z = 8

Squaring on both sides, we get

(x + y + z)2 = 82

x2 + y2 + z2 +2(xy + yz +zx) = 64

⇒ x2 + y2 + z2 = 64 − 2(xy + yz +zx)

= 64 − 2(20) = 64 − 40 = 24

∴ x2 + y2 + z2 = 24

We know that x3 + y3 + z3 − 3xyz = (x + y + z)( x2 + y2 + z2 − xy − yz − zx)

= 8(24 −20) = 8(4) = 32

Answer 2

Answer

(x+y+z)^2 = 5^2

x^2 + y^2 + z^2 + xy + yz + zx = 25

x^2 + y^2 + z^2 = 25 - 10

x^2 + y^2 + z^2 = 15

x^3 + y^3 + z^3 - 3xyz = (x+y+z)(x^2 + y^2 + z^2 - xy- yz - zx)

Put all the values and solve:

x^3 + y^3 + z^3 - 3xyz = 5 (15-10)

= 25