Question

calcular el valor de
curso: Álgebra
con explicación​

Answer 1

Recuerda:

${x}^{a} \times {x}^{b} = {x}^{a + b}$

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

...

${ ({3}^{x}) }^{2} + {( {3}^{y}) }^{2} = 27$

$2 \times {3}^{x} \times {3}^{y} = 22$

Suma las ecuaciones.

${ ({3}^{ x } )}^{2} + 2 \times {3}^{x} \times {3}^{y} + { ({3}^{y} )}^{2} = 49$

${( {3}^{x} + {3}^{y} )}^{2} = {7}^{2}$

${3}^{x} + {3}^{y} = 7$

Por lo tanto:

$( {3}^{x} + {3}^{y} )^{3} = {7}^{3}$

${( {3}^{x} + {3}^{y}) }^{3} = 343$