Question

curso: álgebra
con explicación​

Answer 1

Recuerda:

$(x - y)( {x}^{2} + xy + {y}^{2} ) = {x}^{3} - {y}^{3}$

...

${x}^{2}( {x}^{2} + x + 1) = 9(x - 1)( {x}^{2} + x + 1)$

${x}^{4} + {x}^{3} + {x}^{2} = 9( {x}^{3} - 1)$

${x}^{4} + {x}^{2} + 1 = 8 {x}^{3} - 8$

${x}^{4} + {x}^{2} + 1 = 8( {x}^{3} - 1)$

...

$T= \sqrt{ {8x}^{9} - ( {x}^{4} + {x}^{2} + 1) ( {x}^{6} + {x}^{3} + 1) }$

$T = \sqrt{ {8x}^{9} - \frac{( {x}^{4} + {x}^{2} + 1 )( {x}^{9} - 1) }{( {x}^{3} - 1) } }$

$T = \sqrt{ {8x}^{9} - \frac{8( {x}^{3} - 1)( {x}^{9} - 1) }{ {x}^{3} - 1 } }$

$T = \sqrt{ {8x}^{9} - {8x}^{9} + 8 }$

$T = \sqrt{8}$

$T = 2 \sqrt{2}$

Excelente problema de la cepre, hasta me hizo pensar.