<h2>Problem</h2> <p> If </p> <p style="text-align:center;"> $$ x+\frac{1}{x}=2, $$ </p> <p> find the value of </p> <p style="text-align:center;"> $$ x^5+\frac{1}{x^5}. $$ </p>

 If \x+1/x=2\ Find the value of \x^5+1/x^5\

As we had: `x+1/x=2` `rightarrow(x+1/x)^2=4` `leftrightarrowx^2+1/x^2=2`

We continue with `(x^2+1/x^2)(x+1/x)=4` `leftrightarrowx^3+x+1/x+1/x^3=4`

                                `leftrightarrowx^3+1/x^3=2`

We do that again: `(x^3+1/x^3)(x+1/x)=4` `leftrightarrowx^5+x+1/x+1/x^5=4` 

Therefore, `x^5+1/x^5=2` Because `x+1/x=2`

Solution By: Thin Sokkean

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