Question

Помогите мне найти
$\sqrt{( {x}^{m} + {y}^{m} ) {}^{2} - ( {4}^{ \frac{1}{m} }xy) {}^{m} }$
=????

Answer 1

$\sqrt{(x^{m}+y^{m})^2-(4^{\frac{1}{m}}xy)^{m}}}= \\\\=\sqrt{x^{2m}+2x^{m}y^{m}+y^{2m}-4^{\frac{m}{m}}x^{m}y^{m}} =\\\\= \sqrt{x^{2m}+2x^{m}y^{m}+y^{2m}-4x^{m}y^{m}} = \sqrt{x^{2m}-2x^{m}y^{m}+y^{2m}}=\\\\=\sqrt{(x^{m}-y^{m})^2}=|x^{m}-y^{m}|$