If x + y + z = 19, xy + yz + zx = 114, then the value of √(x3 + y3 + z3 – 3xyz) is:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 19
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Concept |
Understanding |
Application |
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Formula: a3 + b3 + c3 – 3abc = (a + b + c) [(a + b + c)2 – 3(ab + bc + ca)] |
Given x + y + z = 19, xy + yz + zx = 114 |
Applying the formula: x3 + y3 + z3 – 3xyz = 19 × [192 – 3 × 114] = 19 × [361 – 342] = 19 × 19 Hence, √(x3 + y3 + z3 – 3xyz) = 19 |