Value of L in l^2+256-68l
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\begin{lgathered}x + \frac{1}{x} = \sqrt{5} \\ {(x + \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} \\ {( \sqrt{5}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ 5 = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 3 \\ {( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } \\ {(3)}^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ 9 = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 7\end{lgathered}x+x1=5(x+x1)2=x2+x21+2×x×x1(5)2=x2+x21+25=x2+x21+2x2+x21=3(x2+x21)2=x4+x41+2×x2×x21(3)2=x4+x41+29=x4+x41+2x4+x41=7
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