Question

ÁLGEBRA 3 EJERCICIOS 30 PUNTOS

Answer 1

Respuesta:

Pregunta 1

$\frac{ {x}^{8} - {1}^{8} }{ {x}^{m} - {1}^{2} }$

$\frac{8}{m} = \frac{8}{2} \\ 8 \times 2 = m \times 8 \\ 2 = m$

$\frac{ {x}^{8} - {1}^{8} }{ {x}^{2} - {1}^{2} } = \frac{( {x}^{4} - 1)( {x}^{4} + 1)}{( {x}^{2} - 1)} = \frac{( {x}^{2} - 1)( {x}^{2} + 1)( {x}^{4} + 1) }{( {x}^{2} - 1) } \\ \frac{ {x}^{8} - {1}^{8} }{ {x}^{m} - {1}^{2} } = {x}^{6} + {x}^{4} + {x}^{2} + 1$

${m}^{9} + {m}^{8} + m7 + ... + {m}^{2} + m + 1 \\ {m}^{6} ( {m}^{3} + {m}^{2} + m) + {m}^{3} ( {m}^{3} + {m}^{2} + m) + {m}^{3} + {m}^{2} + m + 1 \\ {m}^{3} + {m}^{2} + m( {m}^{6} + {m}^{3} + 1) + 1 \\ m( {m}^{2} + m + 1)( {m}^{6} + {m}^{3} + 1) + 1 \\ 2(4 + 2 + 1)(64 + 8 + 1) + 1 \\ 2(7)(73) + 1 = 1023$

Pregunta 2

$\frac{21}{3} = \frac{35}{5} \\ \frac{7}{1} = \frac{7}{1}\\ t(4) = {({x}^{3})}^{7 - 4} {({y}^{5})}^{4 - 1}\\ t(4)={({x}^{3})}^{3} {({y}^{5})}^{3}\\ t(4) = {x}^{9} {y}^{15}\\ 9 + 15 = 24$