Răspuns:
x+[tex]x+\frac{1}{x}=4[/tex] / ·x
x²+1=4x
x²-4x+1=0
x²-4x+4=3
(x-2)²=3 ⇒ x-2=[tex]\sqrt{3}[/tex]
x=2+[tex]\sqrt{3}[/tex] ⇒
[tex]x^{2} +\frac{1}{x^{2}} =(2+\sqrt{3})^{2} +\frac{1}{(2+\sqrt{3})^{2} } =7+4\sqrt{3} +\frac{(7-4\sqrt{3})/1}{7+4\sqrt{3}} =7+4\sqrt{3} +\frac{7-4\sqrt{3}}{49-48} =7+4\sqrt{3} +7-4\sqrt{3} =14[/tex]
Explicație pas cu pas:
