Question

14. i) If x +1/x = 4,find x2+ 1/x2
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Answer 1

$x + \frac{1}{x} = 4 \\ s.o.b.s \\ squaring \: on \: both \: sides \\ {(x + \frac{1}{x}) }^{2} = {(4)}^{2} \\ we \: know \: that \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2(x)( \frac{1}{x} ) = 16 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 14$