Respuesta:
1/6
Explicación paso a paso:
Si se cumple:
[tex]\sqrt[8]{11.61(6^{4} +5^{4})(6^{8} +5^{8} )+5^{16} } =6^{3-2x}[/tex]
Determina x:
61=6²+5²
11=6²-5²
Resolución:
[tex]\sqrt[8]{(6^{2} -5^{2} )(6^{2} +5^{2}) (6^{4} +5^{4})(6^{8} +5^{8} )+5^{16} } =6^{3-2x}[/tex]
[tex]\sqrt[8]{(6^{4} -5^{4} )(6^{4} +5^{4})(6^{8} +5^{8} )+5^{16} } =6^{3-2x}[/tex]
[tex]\sqrt[8]{(6^{8} -5^{8})(6^{8} +5^{8} )+5^{16} } =6^{3-2x}[/tex]
[tex]\sqrt[8]{(6^{16} -5^{16})+5^{16} } =6^{3-2x}[/tex]
[tex]\sqrt[8]{6^{16} -5^{16}+5^{16} } =6^{3-2x}[/tex]
[tex]\sqrt[8]{6^{16}} =6^{3-2x}\\[/tex]
[tex]6^{\frac{16}{6} } =6^{3-2x}[/tex]
16/6=3-2x
8/3=3-2x
8=9-6x
-1=-6x
1=6x
x=1/6
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