Question

Alguem me ajuda nessa questão

Answer 1

Resposta:

1)$a^{2}+2ac+b^{2}+c^{2}$

2)$\frac{1}{3}$

Explicação passo-a-passo:

1)

$a(a+b+c)+b(b+c-a)+c(a-b+c)\\(a^{2}+ab+ac)+(b^{2}+bc-ba)+(ca-cb+c^{2})\\a^{2}+ab+ac+b^{2}+bc-ba+ca-cb+c^{2}\\\\a^{2}+2ac+b^{2}+c^{2}$

2)

$(\frac{2^{-2} +1^{-2}}{2^{-1} +1^{-1}} ).(\frac{2^{-2} +1^{-3}}{2})^{-1}$

$(\frac{\frac{1}{2^{2}} +\frac{1}{1^{2}} }{\frac{1}{2^{1}} +\frac{1}{1^{1}} } ).(\frac{\frac{1}{2^{2}} +\frac{1}{1^{3}} }{2 } )^{-1}$

$\frac{\frac{\frac{1}{2^{2}} +\frac{1}{1^{2}} }{\frac{1}{2^{1}} +\frac{1}{1^{1}} }}{\frac{\frac{1}{2^{2}} +\frac{1}{1^{3}} }{2 }}$

$\frac{\frac{\frac{5}{4} }{\frac{3}{2} } }{\frac{\frac{1}{4} }{\frac{2}{1} } } =\frac{\frac{5.2}{4.3} }{\frac{5.2}{4.1} } = \frac{5.2.4}{4.3.5.2} =\frac{1}{3}$