If - a-b-c-10 - and - a- 2-b- 2-c- 2-38then -a b-b c-c a isA- 62B- 31C- 64D- 32

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Expansion of (a+b+c)^2

If ∼∼ a+b+c=1...

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$I f a + b + c = 10 a n d a^{2} + b^{2} + c^{2} = 38, t h e n (a b + b c + c a)$ is :

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∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + a b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3. (b - c) (c - a) (a - b) (a + b + c) (a b + b c + c a)

If $a + b + c = 10$ and $a^{2} + b^{2} + c^{2} = 36$ , then $a b + b c + c a =$ .......... .

a + b + c = 10

a^{2} + b^{2} + c^{2} = 38

a b + b c + c a

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + c b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3 (b - c) (c - a) (a - b) (a + b + c) (b c + c a + a b)

a^{2} + b^{2} + c^{2} = 20

a + b + c = 0

a b + b c + c a + 10

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