If x + y + z = 2, xy + yz + zx = -11, then the value of x3+y3+z3-3xyz is:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 74
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Concept |
Understanding |
Application |
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Formula: x3+y3+z3-3xyz = (x+y+z) (x2+y2+z2-xy-yz-zx) and (x+y+z)2 = (x2+y2+z2+2xy+2yz+2xz) |
Given: (x + y + z) = 2 (xy + yz + zx) = -11
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(x + y + z) = 2 (x + y + z)2 = 4 (x2+y2+z2+2xy+2yz+2xz) = 4 (x2+y2+z2 + 2 × -11) = 4 x2+y2+z2 = 4 + 22 = 26 Now, x3+y3+z3-3xyz = (x+y+z) (x2+y2+z2-xy-yz-zx) = 2 × (26 – (-11)) = 2 × 37 = 74 |