If x + y + z = 10, x3 + y3 + z3 = 75 and xyz = 15, then find the value of x2 + y2 + z2 – xy – yz – zx
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 3
| Understanding | Application |
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(x3 + y3 + z3 - 3xyz) = (x + y + z)(x2 + y2 + z2 – xy – yz – zx) Given, x + y + z = 10, x3 + y3 + z3 = 75 and xyz = 15 |
(x3 + y3 + z3 - 3xyz) = (x + y + z)(x2 + y2 + z2 – xy – yz – zx) (75 - 3 x 15) = (10)(x2 + y2 + z2 – xy – yz – zx) (75 - 45) = 10(x2 + y2 + z2 – xy – yz – zx) 30 = 10(x2 + y2 + z2 – xy – yz – zx) (x2 + y2 + z2 – xy – yz – zx) = 30/10 (x2 + y2 + z2 – xy – yz – zx) = 3 |