Question

if (a+b+c)=9 (ab+bc+ca)=40 find a square + b square + c square​

Answer 1

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Answer 2

Answer:

We know that

$\\ \tt {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2 \: (ab + bc \\ \\ \tt + ca) \\ \\ \\ \colon \implies \: \tt {9}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2 \times 40 \\ \\ \\ \colon \implies \: \tt81 = {a}^{2} + {b}^{2} + {c }^{2} + 80 \\ \\ \\ \colon \implies \: \tt {a}^{2} + {b}^{2} + {c}^{2} = 81 - 80 \\ \\ \\ \colon \implies \: \tt \blue{{a}^{2} + {b }^{2} + {c}^{2} = 1}$

Hence,

$\\ \boxed{ \tt{a}^{2} + {b}^{2} + {c}^{2} = 1}$