Question

if x=1/x+2root3, then value of x2-1/x2

Answer 1

Answer:

$8 \sqrt{3}$

Step-by-step explanation:

x-1/x = 2root3

${x}^{2} + {x}^{ - 2} - 2 = 12 \\ {x}^{2} + {x}^{ - 2} = 14 \\ ({x + {x}^{ - 1} })^{2} = 14 + 2 \\ x + {x}^{ - 1} = 4 \\ (x + {x}^{ - 1} )(x - {x}^{ - 1} ) = 4 \times 2 \sqrt{3}$

The second step was obtained by squaring on both sides