Question

x+y+z=19 ,xyz=216 ,xy+yz+zx=114 find
$\sqrt{ {x}^{3} + {y}^{3 + {z}^{3} }$
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Answer 1

Answer:

Step-by-step explanation:

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