Question

O resultado da expressão $\left(-2\right)^2-\left(\dfrac{1}{3}\right)^2:4^2+\left(-\dfrac{1}{2}\right)^2$ é o número real:

Escolha uma:

a. 36/144
b. 144/611
c. 576/144
d. 611/144

Answer 1

Resolvendo:

$\mathsf{=\left(-2\right)^2-\left(\dfrac{-1}{3}\right)^2:4^2+\left(-\dfrac{1}{2}\right)^2}\\\\\\\mathsf{=4-\dfrac{\left(-1\right)^2}{3^2}\div 16+\dfrac{1^2}{2^2}}\\\\\\\mathsf{=4-\dfrac{1}{9}\div 16+\dfrac{1}{4}}\\\\\\\mathsf{=4-\left(\dfrac{1}{9}\div 16\right)+\dfrac{1}{4}}\\\\\\\mathsf{=4-\left(\dfrac{1}{9}\cdot \dfrac{1}{16}\right)+\dfrac{1}{4}}\\\\\\\mathsf{=4-\dfrac{1}{144}+\dfrac{1}{4}}\\\\\\\mathsf{=\dfrac{4\cdot 144}{144}-\dfrac{1}{144}+\dfrac{1\cdot 36}{4\cdot 36}}\\\\\\\mathsf{=\dfrac{576}{144}-\dfrac{1}{144}+\dfrac{36}{144}}\\\\\\\mathsf{=\dfrac{576-1+36}{144}}\\\\\\\mathsf{=\dfrac{576+35}{144}}\\\\\\\mathsf{=\boxed{\dfrac{611}{144}}}\: \: \checkmark$

= = = = =

$\boxed{\mathsf{Resposta:\:Letra\:D}}$