Question

If x2-4x=1, find x2 +1/x2​

Answer 1

Step-by-step explanation:

${x}^{2} - 4x = 1$

$= > {x}^{2} - 1 = 4x$

$= > \frac{ {x}^{2} - 1 }{x} = 4$

$= > \frac{ {x}^{2} }{x} - \frac{1}{x} = 4$

$= > x - \frac{1}{x} = 4$

therefore,

${x}^{2} + \frac{1}{ {x}^{2} } = ( {x - \frac{1}{x} )}^{2} + 2 \times x \times \frac{1}{x}$

$= ( {4)}^{2} + 2$

$= 16 + 2$

$= 18$