If a + b + c = 9 and ab + bc + ca = 15, find : a^2 + b^2 + c^2.

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Solution

Since $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) ∴ (9)^{2} = a^{2} + b^{2} + c^{2} + 2 (15) 81 = a^{2} + b^{2} + c^{2} + 30 ∴ a^{2} + b^{2} + c^{2} = 81 - 30 = 51$ .

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Similar questions

a + b + c = 9

a b + b c + c a = 15

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

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

a + b + c = 9

a b + b c + c a = 24

If $a + b + c = 9$ and $a b + b c + c a = 40$ . Find the value of $a^{2} + b^{2} + c^{2}$ .

a + b + c = 9

a b + b c + c a = 26

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

∣ ∣ ∣ ∣ ∣ \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)

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