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If a = x + y, b = x – y, c = x + 2y, then a2 + b2 + c2 – ab – bc – ca is
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- 4y2
- 5y2
- 6y2
- 7y2
Correct Option: D
a – b = x + y – x + y = 2y
b – c = x – y – x – 2y = – 3y
c – a = x + 2y – x – y = y
Now,
a2 + b2 + c2 – ab – bc – ca
| = | (2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca) | |
| 2 |
| = | [(a − b)2 + (b − c)2 + (c − a)2] | |
| 2 |
| = | [(2y)2 + (−3y)2 + y2] | |
| 2 |
| = | × 14y2 = 7y2 | |
| 2 |
