Answer:
x = 11
Step-by-step explanation:
Given;
[tex]x-\frac{1}{x}=3[/tex]
Squaring equation;
[tex](x-\frac{1}{x})^2=3^2[/tex]
[tex]x^2+\frac{1}{x}^2-2*x*(\frac{1}{x})=9[/tex]
By algebraic identity :
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Substitute
[tex]x^2+\frac{1}{x}^2 - 2 = 9[/tex]
Add
[tex]x^2 + \frac{1}{x}^2 = 9 +2[/tex]
Simplify
[tex]x^2 + \frac{1}{x}^2 = 11[/tex]
Hence, x = 11.
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