Răspuns:
Explicație pas cu pas:
a.
[tex]x+\frac{1}{x}-5=0, x^{2} -5x+1=0[/tex]
[tex]x_{1}=\frac{5+\sqrt{21} }{2} > 0\\x_{2}=\frac{5-\sqrt{21} }{2} > 0[/tex]
b.
[tex]x+\frac{1}{x}=5\\(x+\frac{1}{x})^{2} =25\\x^{2} +(\frac{1}{x} )^{2} +2=25\\x^{2} +\frac{1}{x^{2} } =23[/tex]
[tex]x^{2} +\frac{1}{x^{2} } =23[/tex]
[tex](x^{2} +\frac{1}{x^{2} })^{2} =529\\x^{4}+\frac{1}{x^{4} }+2=529\\x^{4}+\frac{1}{x^{4} }=527[/tex]
c.
[tex](x+\frac{1}{x} )^{3}=x^{3} +\frac{1}{x^{3} }+3x+\frac{3}{x} \\x^{3} +\frac{1}{x^{3} }=(x+\frac{1}{x} )^{3}-3(x+\frac{1}{x})=5^{3}-3*5= 110[/tex]
