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If ab + bc + ca = 0 then the value of 1 + 1 + 1 is ( a² - bc ) ( b² - ac ) ( c² - ab )
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- 0
- 1
- 3
- a + b + c
- 0
Correct Option: A
ab + bc + ca = 0
⇒ ab + ca = – bc
∴ a2 – bc = a2 + ab + ac = a(a + b + c)
Similarly,
b2 – ca = b(a + b + c)
c2 – ab = c(a + b + c)
| ∴ Expression = | + | + | ||||
| ( a² - bc ) | ( b² - ac ) | ( c² - ab ) |
| Expression = | + | + | ||||
| a(a + b + c) | b(a + b + c) | c(a + b + c) |
| Expression = |  | + | + |  | |||||
| (a + b + c) | a | b | c |
| Expression = | | | |||
| (a + b + c) | abc |
| Expression = | × | | | = 0 | ||
| (a + b + c) | abc |
