Question

Productos Notables: Resolver el siguiente ejercicio...

Answer 1

Recuerda que:

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

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

...

$( { \sqrt{n} }^{2} + 2( \sqrt{n} )( \sqrt{m} ) + { \sqrt{m} }^{2} )( { \sqrt{n} }^{2} - 2( \sqrt{n} )( \sqrt{m} ) + { \sqrt{m} }^{2} ) = 0 \\ {( \sqrt{n} + \sqrt{m} )}^{2} {( \sqrt{n} - \sqrt{m}) }^{2} = 0 \\ {( { \sqrt{n} }^{2} - \sqrt{m} }^{2})^{2} = 0 \\ {(n - m)}^{2} = 0 \\ n - m = 0 \\ n = m$

Ahora solo reemplaza todo con una sola variable.

$= \frac{n + 5n}{n + n} + \frac{ {n}^{3} n + {n}^{4} }{n {n}^{3} + {n}^{2} {n}^{2} } \\ = \frac{6n}{2n} + \frac{ {2n}^{4} }{ {2n}^{4} } \\ = 3 + 1 \\ = 4$