Question

if x+y +z=6xy+yz+zx=11,then find the value of x3y3z3-3xyz​

Answer 1

Answer:

18

Step-by-step explanation:

Given x + y + z = 6 and xy + yz + zx = 11

Consider, x + y + z = 6

Squaring on both sides, we get

(x + y + z)2 = 36

x2 + y2 + z2 +2(xy + yz +zx) = 36

⇒ x2 + y2 + z2 = 36 − 2(xy + yz +zx)

= 36 − 2(11) = 36-22 = 14

∴ x2 + y2 + z2 = 14

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

= 6(14 −11) = 6(3) = 18

Answer 2

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