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If a + b + c = 6 and ab + bc + ca = 11, then the value of bc (b + c) + ca (c + a) + ab (a + b) + 3abc is
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- 33
- 66
- 55
- 23
Correct Option: B
a + b + c = 6 and ab + bc + ca = 11
∴ bc (b + c) + ca (c + a) + ab (a + b) + 3abc
= bc (b + c) + abc + ca (c + a) + abc + ab (a + b) + abc
= bc (a + b + c) + ca (a + b + c) + ab (a + b + c)
= (a + b + c) (bc + ca + ab)
= 6 × 11 = 66
