Question

a)Aratati ca numarul A=radical mare din (18^2+24^2 )/(6^2+8^2) +2*radical mare din 26^2-24^2 este natural
b)Descompuneti in factori : 4x^3-24x^2+36x

Answer 1

Salut,

$A=\sqrt{\dfrac{18^2+24^2}{6^2+8^2}}+2\sqrt{26^2-24^2}=\sqrt{\dfrac{(3\cdot 6)^2+(3\cdot 8)^2}{6^2+8^2}}+\\\\+2\sqrt{(26-24)(26+24)}=\sqrt{\dfrac{3^2\cdot 6^2+3^2\cdot 8^2}{6^2+8^2}}+2\sqrt{2\cdot 50}=\\\\=\sqrt{\dfrac{3^2(6^2+8^2)}{6^2+8^2}}+2\sqrt{100}=\sqrt{3^2}+2\cdot 10=23\in\mathbb{N}.$

La punctul b), dacă dai pe 4x factor comun, ce obții ?

Green eyes.