Question

Si 2^x + 2^y = a
x + y = 4
entonses 4^x + 4^y equivale
Ayuda porfa

Answer 1

Explicación paso a paso:

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

$(2^x) {}^{2} + {2}\times{2}^{x} \times {2}^{y} + \: (2^y ) {}^{2} = {a}^{2}$

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

${4}^{x} + {2}\times {2}^{4} + {4}^{y} = {a}^{2}$

${4}^{x} + {2}\times16 + {4}^{y} = {a}^{2}$

${4}^{x} + {4}^{y} = {a}^{2} - 32$