Question

Se m e n são raízes de x² – 4x + 12 = 0, então 1/m + 1/n vale
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Answer 1

$\boxed{\begin{array}{l}\sf x^2-4x+12=0\\\sf s=-\dfrac{b}{a}~~p=\dfrac{c}{a}\\\\\sf m+n=-\dfrac{-4}{1}=4\\\\\sf m\cdot n=\dfrac{12}{1}=12\\\\\sf \dfrac{1}{m}+\dfrac{1}{n}=\dfrac{m+n}{m\cdot n}\\\\\sf\dfrac{1}{m}+\dfrac{1}{n}=\dfrac{4}{12}=\dfrac{1}{3}\end{array}}$