Question

ayudaaa con resolución porfa ​

Answer 1

Respuesta:

$m^{4} + n^{4} = 3$

Explicación paso a paso:

$m+n=\sqrt{7}$         $mn=1$

$(m+n)^{2}=\sqrt{7}^{2}$

$m^{2} + 2mn +n^{2} = 7$

$m^{2} +2(1) +n^{2} =7$

$m^{2}+ n^{2} =5$

Hallar : $m^{4} +n^{4}$

$(m^{2} + n^{2})^{2} = (5)^{2}$

$(m^{2)} ^{2} + 2(m^{2})^{2}(n^{2})^{2} +(n^2)^2=5$

$m^{4} + 2m^{4} n^{4} + n^{4} = 5$

$m^{4} + 2(mn)^{4} + n^{4} = 5$

$m^{4} +2(1)^{2} + n^{4} =5$

$m^{4} + n^{4} = 3$