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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
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- 2
Correct Option: C
ab + bc + ca = 0
⇒ ab + ca = – bc
∴ a2 – bc = a2 + ab + ca
⇒ a2 – bc = a (a + b + c)
Similarly,
b2 – ac = 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 = | = 0 { ∴ ab + bc + ca = 0 } | |
| abc (a + b + c) |
