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Algebraic Identity: (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac

If a + b + c...

Question

If a + b + c = 12 and $a^{2} + b^{2} + c^{2} = 50$ ; find ab + bc + ca

A

24

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B

94

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C

48

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D

47

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Solution

The correct option is D
47

Given that

$a + b + c = 12;$
Squaring on both sides , we have
$(a + b + c)^{2} = 12^{2}$
$a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 144$
Given $a^{2} + b^{2} + c^{2} = 50$ ;
$50 + 2 (a b + b c + c a) = 144$
$2 (a b + b c + c a) = 94$
$(a b + b c + c a) = 47$

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Q. If a² + b² + c² + ab + bc + ca = 89 and (a + b) : (b + c) : (c + a) = 12 : 5 : 3, where a, b and c are real numbers, then (a² + b² + c² – ab – bc – ca) equals

यदि a² + b² + c² + ab + bc + ca = 89 तथा (a + b) : (b + c) : (c + a) = 12 : 5 : 3, जहाँ a, b व c वास्तविक संख्याएँ हैं, तब (a² + b² + c² – ab – bc – ca) बराबर है

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