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If x = z = 225 and y = 226 then the value of x3 + y3 + z3 - 3xyz is :
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- 765
- 676
- 576
- 674
- 765
Correct Option: B
Using Rule 22,
x = z = 225, y = 226
∴ x + y + z = 225 + 226 + 225 = 676
| ∴ x3 + y3 + z3 – 3 xyz = | (x + y + z) [ (x - y)2 + (y - z)2 + (z - x)2 ] | |
| 2 |
| ⇒ x3 + y3 + z3 – 3 xyz = | × 676 × [ (225 – 226)2 + (226 – 225)2 + (225 – 225)2 ] | |
| 2 |
| ⇒ x3 + y3 + z3 – 3 xyz = | × 676 × (1 + 1) = 676 | |
| 2 |
