Question

СРОЧНО! ПОМОГИТЕ! 35б​

Answer 1

$1)\ \ \sqrt[3]{x}-\sqrt[6]{x}-30=0\ \ ,\ \ \ ODZ:\ x\geq 0\\\\t=\sqrt[6]{x}\geq 0\ \ ,\ \ \ t^2-t-30=0\ \ ,\ \ t_1=-5\ ,\ t_2=6\ \ \ (teorema\ Vieta)\\\\\sqrt[6]{x}=6\ \ \to \ \ \ x=6^6\ \ ,\ \ \ \boxed {\ x=46656\ }$

$2)\ \ \sqrt{x}+7\sqrt[4]{x}-18=0\ \ ,\ \ \ ODZ:\ x\geq 0\ ,\\\\t=\sqrt[4]{x}\geq 0\ \ ,\ \ \ t^2+7t-18=0\ \ ,\ \ \ t_1=-9\ ,\ t_2=2\ \ (teorema\ Vieta)\\\\\sqrt[4]{x}=2\ \ ,\ \ x=2^4\ \ ,\ \ \boxed {\ x=16\ }$