Question

6. If a + b + c =9 and ab + bc + ca = 26, find a²+b²+c²​

Answer 1

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${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ {9}^{2} = {a}^{2} + {b}^{2} + {c}^{2} +2 \times 26 \\ 81 = {a}^{2} + {b}^{2} + {c}^{2} +52 \\ 81 - 52 = {a}^{2} + {b}^{2} + {c}^{2} \\ {a}^{2} + {b}^{2} + {c}^{2} = 29 \: ans$

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Answer 2

Answer:

29

Step-by-step explanation:

(a+ b+ c)² = a² + b² + c² + 2ab + 2b + 2ca

(9)² = a² + b² + c² + 2(ab + bc + ca)

(9)² = a² + b² + c² + 2(26)

81 = a² + b² + c² + 52

a² + b² + c² = 81 - 52

a² + b² + c² = 29

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