Question

Найдите f(x), если f(x+1/x)=x^2+1/x^2 $f(x+ frac{1}{x})= x^{2} + frac{1}{ x^{2} }$

Answer 1

$f(x)=?\f(x+frac{1}{x})=x^2+frac{1}{x^2}$

$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$

Answer 2

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