Question

If a+b+c =9 , ab + bc+ca=26
a
${a}^{2} + {b}^{2} + {c}^{2} = x$


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Answer 1

Use the formula $(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)$

$(9)^2 = x+2(26)$

$81 = x + 52$

$x+52 = 81\\x = 81-52\\x = 29$

∴ a^2 + b^2 + c^2 = 29