Question

Factorise :- the question below answer it step wise

Answer 1

${x}^{4} + \frac{1}{ {x}^{4} } + 1 \\ \\ \\ : \longrightarrow \: {( {x}^{2}) }^{2} + \frac{1}{ {( {x}^{2}) }^{2} } + 2 {x}^{2} \frac{1}{ {x}^{2} } - 2+ 1 \\ \\ \\ : \longrightarrow { \bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg) }^{2} - {\bigg(1 \bigg)}^{2} \\ \\ \\ : \longrightarrow \bigg( {x}^{2} + \frac{1}{ {x}^{2} } + 1 \bigg) \bigg( {x}^{2} + \frac{1}{ {x}^{2} } - 1 \bigg) \\ \\ \\ : \longrightarrow\bigg( {x}^{2} + \frac{1}{ {x}^{2} } + 2x \frac{1}{x} - 1\bigg) \bigg( {x}^{2} + \frac{1}{ {x}^{2} } + 2x \frac{1}{x} + 1 \bigg) \\ \\ \\ : \longrightarrow \bigg \{{\bigg(x + \frac{1}{x} \bigg)}^{2} - 1 \bigg \} \bigg \{ {\bigg(x + \frac{1}{ x} \bigg)}^{2} + 1 \bigg \} \\ \\ \\ : \longrightarrow \bigg(x + \frac{1}{x} + 1 \bigg) \bigg(x + \frac{1}{x} - 1 \bigg)\bigg \{ {\bigg(x + \frac{1}{ x} \bigg)}^{2} + 1 \bigg \}$