Question

URGENTE!! Se A e B são as raízes da equação: 15x² - 7x + 12 = 0, o valor de 1/a + 1/b é.
A) 7/12
B)-7/12
C)-15/12
D)15/12
E)-3/4​

Answer 1

$\large\boxed{\begin{array}{l}\rm Se~A~e~B~s\tilde ao~ra\acute izes~da\\\rm equac_{\!\!,}\tilde ao:~15x^2-7x+12=0,\\\rm o~valor~de~\dfrac{1}{A}+\dfrac{1}{B}~\acute e:\\\tt a)\dfrac{7}{12}\\\tt b)-\dfrac{7}{12}\\\\\tt c)-\dfrac{15}{12}\\\\\tt d)\dfrac{15}{12}\\\\\tt e)-\dfrac{3}{4}\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf 15x^2-7x+12=0\\\sf A+B=-\dfrac{-7}{15}=\dfrac{7}{15}\\\\\sf A\cdot B=\dfrac{12}{15}\\\\\sf\dfrac{1}{A}+\dfrac{1}{B}=\dfrac{A+B}{A\cdot B}\\\\\sf\dfrac{1}{A}+\dfrac{1}{B}=\dfrac{\frac{7}{\diagdown\!\!\!\!\!\!15}}{\frac{12}{\diagdown\!\!\!\!\!\!15}}\\\\\sf\dfrac{1}{A}+\dfrac{1}{B}=\dfrac{7}{12}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~A}}}}\end{array}}$