Question

Determine o valor numérico das seguintes expressões algébricas:​

Answer 1

Explicação passo-a-passo:

$a) \frac{ {( - 1)}^{2} - 2 \times ( - 1) - 3}{ {( {( - 1)}^{2} + 3) }^{4} } = \frac{1 + 2 - 3}{ {(1 + 3)}^{4} } = \\ \\ \frac{3 - 3}{ {4}^{4} } = \frac{0}{256} = 0 \\ \\ \\ b) {( \frac{1}{2} )}^{3} - 2 \times {( \frac{1}{2} - 1)}^{2} + 5 \times \frac{1}{2} - 2 = \\ \\ \frac{1}{8 } - 2 \times {( \frac{1 - 2}{2}) }^{2} + \frac{5}{2} - 2 = \\ \\ \frac{1}{8} - 2 \times {( - \frac{1}{2} )}^{2} + \frac{5}{2} - 2 = \\ \\ \frac{1}{8} - 2 \times \frac{1}{4} + \frac{5}{2} - 2 = \\ \\ \frac{1}{8} - \frac{2}{4} + \frac{5}{2} - 2 = \frac{1 - 4 + 20 - 16}{8} = \\ \\ \frac{ - 3 + 4}{8} = \frac{1}{8} \\ \\ \\ c) \sqrt{5 - 2 \times \frac{1}{2} } + \frac{5}{2} = \sqrt{5 - \frac{2}{2} } + \frac{5}{2} = \\ \\ \sqrt{5 - 1} + \frac{5}{2} = \sqrt{4} + \frac{5}{2} = 2 + \frac{5}{2} = \\ \\ \frac{4 + 5}{2} = \frac{9}{2} \\ \\ \\ d) \frac{ {( \frac{1}{2}) }^{2} + {2}^{2} + {( - 1)}^{2} }{ - {( \frac{1}{2}) }^{2} - {2}^{2} - {( - 1)}^{2} } = \frac{ \frac{1}{4} + 4 + 1}{ - \frac{1}{4} - 4 - 1 } = \\ \\ \frac{ \frac{1 + 16 + 4}{4} }{ \frac{ - 1 - 16 - 4}{4} } = \frac{ \frac{21}{4} }{ \frac{ - 21}{4} } = \frac{21}{4} \times ( - \frac{4}{21} ) = - 1$