Question

I'll give brainy to correct

Answer 1

Hey mate
By using the identity
$(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab$
so we have
$x + \frac{1}{x} = 6$
squaring both sides

$(x + \frac{1}{x} ) {}^{2} = (6) {}^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 36$
cancelling x in multiplication we have
${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 36 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 36 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 34$
repeating the process we have
$( {x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = (34) {}^{2} \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 1156 \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 1156 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 1156 - 2 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 1154$
1154 is your answer
Hope it helps dear friend ☺️✌️✌️