If $x + y + z = 6$ and $(x y + y z + z x) = 11$ , then what is the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ ?

18

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36

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54

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66

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Solution

The correct option is A $18$
$x^{3} + y^{3} + z^{3} - 3 x y z = (x + y + z) [(x + y + z)^{2} - 3 (x y + y z + z x)]$
$\Rightarrow x^{3} + y^{3} + z^{3} - 3 x y^{3} = 6 [6^{2} - 3 (11)] = 18$

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x + y + z = 7, x y + y z + z x = 16

x^{3} + y^{3} + z^{3} - 3 x y z

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x y + y z + z x = 12

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If x+y+z=6 and xy+yz+zx=12 then show that x³+y³+z3=3xyz

pls send the answer fast

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