If a = 355, b = 356, c = 357, then find the value of a3 + b3 + c3 – 3abc.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 3204.
| Understanding/Application |
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a = 355, b = 356, c = 357 a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca) |
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= 1/2(a + b + c) (2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca) = 1/2[(a + b + c) {(a - b)2 + (b - c)2 + (c - a)2}] = 1/2[(355 + 356 + 357) {(355 - 356)2 + (356 - 357)2 + (357 - 355)2] = 1/2[(1068 (1 + 1 + 4) = 3204 |