Answer:
Step-by-step explanation:
[tex]a + \frac{1}{2}=4\\\\[/tex]
[tex]a = 4 -\frac{1}{2}\\\\a =\frac{4*2}{1*2}-\frac{1}{2}\\\\a =\frac{8}{2}-\frac{1}{2}\\\\a=\frac{7}{2}[/tex]
[tex]\frac{1}{a}=\frac{1}{\frac{7}{2}}\\\\ = 1*\frac{2}{7}\\\\ = \frac{2}{7}[/tex]
[tex]a^{3}+\frac{1}{a^{3}}=(\frac{7}{2})^{3}+(\frac{2}{7})^{3}[/tex]
[tex]= \frac{343}{8}+\frac{8}{343}\\\\=\frac{343*343}{8*343}+\frac{8*8}{343*8}\\\\=\frac{117649}{2744}+\frac{64}{2744}\\\\=\frac{117649+64}{2744}\\\\=\frac{117713}{2744}\\\\= 42\frac{2465}{2744}[/tex]
