Respuesta:
E) 0,25
Explicación paso a paso:
[tex]\frac{a^{3} +b^{3} +c^{3} }{12.a.b.c} =\frac{(\sqrt{5} -\sqrt[3]{2}+1 )^{3} +(\sqrt[3]{2} -4)^{3} +(3-\sqrt{5} )^{3} }{12.(\sqrt{5} -\sqrt[3]{2}+1)(\sqrt[3]{2} -4)(3-\sqrt{5})}[/tex]
[tex]= \frac{(2,23-1,26+1)^{3} + (1,26-4)^{3} + (3-2,23)^{3} }{12(1,97)(-2,74)(0,77)}[/tex]
[tex]= \frac{(1,97)^{3} + (-2,74)^{3} + (0,77)^{3} }{12(-4,16)}[/tex]
[tex]= \frac{(7,65) + (-20,57) + (0,46) }{-49,92}[/tex]
[tex]= \frac{-12,46 }{-49,92}[/tex]
[tex]= 0,25[/tex]
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Verified answer
Respuesta:
E) 0,25
Explicación paso a paso:
[tex]\frac{a^{3} +b^{3} +c^{3} }{12.a.b.c} =\frac{(\sqrt{5} -\sqrt[3]{2}+1 )^{3} +(\sqrt[3]{2} -4)^{3} +(3-\sqrt{5} )^{3} }{12.(\sqrt{5} -\sqrt[3]{2}+1)(\sqrt[3]{2} -4)(3-\sqrt{5})}[/tex]
[tex]= \frac{(2,23-1,26+1)^{3} + (1,26-4)^{3} + (3-2,23)^{3} }{12(1,97)(-2,74)(0,77)}[/tex]
[tex]= \frac{(1,97)^{3} + (-2,74)^{3} + (0,77)^{3} }{12(-4,16)}[/tex]
[tex]= \frac{(7,65) + (-20,57) + (0,46) }{-49,92}[/tex]
[tex]= \frac{-12,46 }{-49,92}[/tex]
[tex]= 0,25[/tex]