Question

ajudaaaaaa pelo amor de Deus​

Answer 1

Resposta:

Explicação passo-a-passo:

Elevando ambos os membros da primeira equação ao quadrado teremos:

$(\dfrac{1}{a}+\dfrac{1}{b})^{2}=4^{2}\\\\\dfrac{1}{a^{2}}+2.\dfrac{1}{a}.\dfrac{1}{b}+\dfrac{1}{b^{2}}=16\\\\\\\dfrac{1}{a^{2}}+\dfrac{2}{ab}+\dfrac{1}{b^{2}}=16\\\\reagrupando\\\\\dfrac{1}{a^{2}}+\dfrac{1}{b^{2}}+\dfrac{2}{ab}=16\\\\mas\\\\\dfrac{1}{a^{2}}+\dfrac{1}{b^{2}}=\dfrac{17}{2}\\\\substituindo\\\\\dfrac{17}{2}+\dfrac{2}{ab}=16\\\\\dfrac{2}{ab}=16-\dfrac{17}{2}\\\\\dfrac{2}{ab}=\dfrac{32-17}{2}\\\\\dfrac{2}{ab}=\dfrac{15}{2}\\\\ab=\dfrac{2.2}{15}$

$\boxed{ab=\dfrac{4}{15}}$