Resposta:
[tex] {48x}^{4} + {16x}^{2} = 64[/tex]
[tex] {48x}^{4} + 16 {x}^{2} - 64 = 0[/tex]
[tex]( {48x}^{2} )^{2} + {16x}^{2} - 64 = 0[/tex]
[tex] {x}^{2} = y[/tex]
[tex] {48y}^{2} + 16y - 64 = 0[/tex]
[tex]a = 48 \: \: \: b = 16 \: \: \: e \: \: \: c = - 64[/tex]
[tex]x = \frac{ - ( + 16) \frac{ + }{ - } \sqrt{ {16}^{2} - 4 \times 48 \times ( - 64)} }{2 \times 48} [/tex]
[tex]x = \frac{ - 16 \frac{ + }{ - } \sqrt{12544} }{96} [/tex]
[tex]x = \frac{ - 16 \frac{ + }{ - } 112}{96} [/tex]
[tex]x1 = \frac{ - 16 + 112}{96} = \frac{96}{96} = 1[/tex]
[tex]x2 = \frac{ - 16 - 112}{96} = \frac{ - 128}{96} = \frac{4}{3} [/tex]
[tex] {x}^{2} = 1[/tex]
[tex]x = \frac{ + }{ - } \sqrt{1} [/tex]
[tex]x = \frac{ + }{ -} 1[/tex]
[tex] {x}^{2} = \frac{4}{3} [/tex]
[tex]x = \frac{ + }{ - } \sqrt{ \frac{4}{3} } [/tex]
[tex]x = \frac{ + }{ - } \frac{2}{ \sqrt{3} } [/tex]
[tex]x = \frac{ + }{ - } \frac{2 \sqrt{3} }{3} [/tex]
S = { 2\/3/3, - 2\/3/3, 1 , - 1}
Espero ter ajudado.
