Question
If x + y + z = 7, x² + y² + z² = 85 and
x³ + y³ + z³ = 842, then the value of √3 xyz is:Solution
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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