If x + y + z = 7, x² + y² + z² = 85 and x³ + y³+ z³ = 842, then the value of√3 xyz is:
x³ + y³+ z³ - 3xyz = (x+y+z)× 1/2 [3( x² + y² + z²) - (x + y + z)2] => 842 - 3xyz = 7× 1/2 [3 × 85 - 49] => 842 - 3xyz = 7× 103 => 3xyz = 842 - 721 => 3xyz = 121 =>√3 xyz = √121 = 11
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