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If 2s = a + b + c, then the value of s(s – c) + (s – a) (s – b) is
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- ab
- abc
- 0
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a + b + c 2
Correct Option: A
2s = a + b + c
| ∴ s (s – c) = |  |  | | − c | | ||
| 2 | 2 |
| = | |
| 4 |
Again, (s – a) (s – b)
| = | (2s – 2a) (2s – 2b) | |
| 4 |
| = | (a + b + c – 2a) (a + b + c – 2b) | |
| 4 |
| = | (b + c – a) (a + c – b) | |
| 4 |
∴ s (s – c) + (s – a) (s – b)
| = | [(a + b + c) (a + b – c) + (b + c – a) (a + c – b)] | |
| 4 |
| = | [(a + b)2 – c2 + ab + ac – a2 + bc + c2 – ac – b2 – bc + ab] | |
| 4 |
| = | (a2 + b2 + 2ab – c2 + ab + ac – a2 + bc + c2 – ac – b2 – bc + ab) | |
| 4 |
| = | × 4ab = ab | |
| 4 |
