Найдите f(x), если f(x+1/x)=x^2+1/x^2 [tex]f(x+ \frac{1}{x})= x^{2} + \frac{1}{ x^{2} } [/tex]

[tex]f(x)=?\\f(x+\frac{1}{x})=x^2+\frac{1}{x^2}[/tex]

[tex]x+\frac{1}x=t\\(x+\frac{1}x)^2=t^2\\x^2+2*\frac{1}{x}*x+\frac{1}{x^2}=t^2\\x^2+\frac{1}{x^2}=t^2-2\\\\f(x)=x^2-2[/tex]