[tex]\frac{1}{x}+x = 5 \ \ |()^{2}\\\\(\frac{1}{x}+x})^{2} = 5^{2}\\\\(\frac{1}{x})^{2}+2\cdot\frac{1}{x}\cdot x+x^{2} = 25\\\\\frac{1}{x^{2}}+2\cdot\frac{1}{x}\cdot x+x^{2} = 25\\\\\frac{1}{x^{2}}+2+x^{2} = 25\\\\\frac{1}{x^{2}}+x^{2}=25-2\\\\\underline{\frac{1}{x^{2}}+x^{2} = 23}\\\\\boxed{Odp. \ A}[/tex]
Wykorzystano wzór skróconego mnożenia:
[tex](a+b)^{2} = a^{2}+2ab+b^{2}[/tex]
