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Algebraic Identities

If a+b+c=5 an...

Question

If $a + b + c = 5$ and $a b + b c + c a = 4$ ,then the value of $a^{2} + b^{2} + c^{2}$ is ______.

A

25

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B

18

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C

17

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D

9

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Solution

The correct option is C 17
$a^{2} + b^{2} + c^{2} = (a + b + c)^{2} - 2 (a b + b c + c a)$
$a^{2} + b^{2} + c^{2} = (5)^{2} - 2 (4) = 25 - 8 = 17$

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a - b + c = 5

c a - a b - b c = 7,

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\frac{a^{2} + b^{2} + a b}{b^{2} + c^{2} + b c} + \frac{c^{2} + c a + a^{2}}{b^{2} + c^{2} + b c}

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, then the value of

- (\frac{a^{2} + b^{2} + c^{2}}{b c + c a + a b})

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