Question

Dados a=2^0-4^-1, b=4^0-2^-1 e c=2^0+2^-1, calcule o valor de:


a) a+b

b) b-c

c) a x c

com cálculo por favor

Answer 1

a) a+b=

$(2^{0} -4^{-1} )+(4^{0} -2^{-1} )=\\1-(\frac{1}{4})^{1} +1-(\frac{1}{2}) ^{1} =\\1-\frac{1}{4} +1-\frac{1}{2} =\\\frac{4-1+4-2}{4} =\\\frac{5}{4}$

b) b-c=

$(4^{0} -2^{-1} )-(2^{0} +2^{-1} )=\\1-(\frac{1}{2} )^{1} -(1+(\frac{1}{2} )^{1} )=\\1-\frac{1}{2} -(1+\frac{1}{2} )=\\\frac{2-1}{2} -(\frac{2+1}{2} )=\\\frac{1}{2} -\frac{3}{2} =\\\frac{-2}{2} =\\-1$

c) a.c=

$(2^{0} -4^{-1} ).(2^{0} +2^{-1} )=\\(1-(\frac{1}{4} )^{1} ).(1+(\frac{1}{2} )^{1} )=\\(1-\frac{1}{4} ).(1+\frac{1}{2} )=\\(\frac{4-1}{4} ).(\frac{2+1}{2} )=\\(\frac{3}{4} ).(\frac{3}{2} )=\\\frac{9}{8}$