Question

Ayúdenme en esta tarea. ;)

Answer 1

Respuesta:

$\bold{576 \: \: {m}^{2} }$

Explicación paso a paso:

Calculado:

$\bold{M = \sqrt[8]{1+35(6^2 + 1)(6^4 + 1 )(6^8 + 1) }}$

$\bold{M = \sqrt[8]{1+5(7)(6^2 + 1^2)(6^4 + 1^4 )(6^8 + 1^8) }}$

$\bold{M = \sqrt[8]{1+5(6 + 1)(6^2 + 1^2)(6^4 + 1^4 )(6^8 + 1^8) }}$

Recordar que:

$\boxed{ \bold{(a+b)(a^2 + b^2 )(a^4 + b^4 )(a^8 + b^8 ) = \frac{ a^{16} - b^{16}}{a-b}}}$

Entonces:

$\bold{M = \sqrt[8]{1+5 \red{(6 + 1)(6^2 + 1^2)(6^4 + 1^4 )(6^8 + 1^8) }}}$

$\bold{M = \sqrt[8]{1+5 \red{ \left ( \frac{ {6}^{16} - {1}^{16} }{6 - 1} \right ) }}}$

$\bold{M = \sqrt[8]{1+ \cancel{5 } \left ( \frac{ {6}^{16} - 1}{ \cancel{5}}\right ) }}$

$\bold{M = \sqrt[8]{ \cancel{1}+ ({6}^{16} - \cancel{1})}}$

$\bold{M = \sqrt[8]{ {6}^{16} }}$

$\bold{M = {6}^{ \frac{16}{8} } }$

$\bold{M = {6}^{2} }$

$\boxed{\bold{M = 36}}$

Calculando:

$\bold{N = \left ( 1 + \sqrt{18} + \sqrt{6} + \sqrt{3} \right ) \left ( \sqrt{18} + 1 - \sqrt{3} - \sqrt{6} \right )}$

$\bold{N = \left [ ( 1 + \sqrt{18} )+( \sqrt{6} + \sqrt{3}) \right ] \left [ ( 1+\sqrt{18} )-( \sqrt{6} + \sqrt{3} ) \right ]}$

Producto notable:

$\boxed{ \bold{(a+b)(a-b) = a^2 - b^2 }}$

Entonces:

$\bold{N = \left [ ( 1 + \sqrt{18} )+( \sqrt{6} + \sqrt{3}) \right ] \left [ ( 1+\sqrt{18} )-( \sqrt{6} + \sqrt{3} ) \right ]}$

$\bold{N = \left ( 1 + \sqrt{18} \right ) ^2 - \left ( \sqrt{6} + \sqrt{3} \right ) ^2 }$

$\bold{N = \left ( 1^2 + 2(1)(\sqrt{18})+ \sqrt{18}^2 \right ) - \left ( \sqrt{6}^2 + 2(\sqrt{6} )(\sqrt{3} )+ \sqrt{3}^2 \right ) }$

$\bold{N = \left ( 1 + 2\sqrt{18}+ 18 \right ) - \left ( 6 + 2\sqrt{18} + 3 \right ) }$

$\bold{N = \left ( 19 + 2\sqrt{18} \right ) - \left ( 9+ 2\sqrt{18} \right ) }$

$\bold{N = 19 + \cancel{2\sqrt{18} }- 9 - \cancel{ 2\sqrt{18} }}$

$\bold{N = 19- 9 }$

$\boxed{\bold{N = 10}}$

Omar quiere construir una piscina rectangular, cuyas dimensiones son (M-4) y (N+8)

Determina el área de la piscina:

$\bold{A_{ \boxed{ \: }}= (M-4) \cdot (N+8)}$

$\bold{A_{ \boxed{ \: }} = (36 - 4) \cdot (10+8)}$

$\bold{A_{ \boxed{ \: }} = (32) \cdot (18)}$

$\bold{A_{ \boxed{ \: }} =576}$