Question

Arătați că: Radical 2¹⁰ + 2¹³ € tăiat I

Answer 1

Salut,

$2^{10}+2^{13}=2^{10}+2^{3+10}=2^{10}+2^3\cdot 2^{10}=2^{10}+8\cdot 2^{10}=9\cdot 2^{10}=\\\\=3^2\cdot 2^{5\cdot 2}=3^2\cdot (2^5)^2=(3\cdot 2^5)^2.\\\\ Deci\ \sqrt{2^{10}+2^{13}}=\sqrt{(3\cdot 2^5)^2}=3\cdot 2^5,\ care\ NU\ este\ num\breve{a}r\ ira\c{t}ional.$

Ai înțeles rezolvarea ?

Green eyes.