Question

fie numarul a= 17+ x√3 . pentru ce valoare reala a lui x numarul a este rational ?

Answer 1

 [tex]a=17+x\sqrt3\;\in\;\mathbb{Q}\;\;\;dac\u{a}\;\;x=M_{\sqrt3}\;;\\ Verificare:\;\;a=17+M_{\sqrt3}\cdot\sqrt3=17+M_{3}\,\in\,\mathbb{Q}[/tex]

Answer 2

x=0 ⇒ a=17+0*√3⇒ a=17 ∈Q
x=√3⇒a=17+√3*√3=17+3=20 ∈Q
x=2√3⇒ a=17+2√3*√3=17+2*3=17+6=23∈Q
x=3√3⇒ a=17+3*√3*√3=17+3*3=17+9=26
x=k√3, K∈N