Question

Решите уравнение : x в 4степени=80

Answer 1

$x^4=80\\\\x^4-80=0\\\\(x^2-\sqrt{80})(x^2+\sqrt{80})=0,\\\\\sqrt{80}=\sqrt{16\cdot 5}=4\sqrt5\\\\(x-\sqrt{4\sqrt{5}})(x+\sqrt{4\sqrt{5}})(x^2+4\sqrt5)=0\\\\(x-2\sqrt[4]5)(x+2\sqrt[4]{5})(x^2+4\sqrt5)=0\\\\x_1=2\sqrt[4]{5},\; x_2=-2\sqrt[4]{5}$