Question

if x=3-2root2,find the value of x^3+1/x^3

Answer 1

Solution:-

given by:-

$x = 3 - 2\sqrt{2} \\ {x}^{3} + \frac{1}{ {x}^{3} } \\ {x}^{3} = {(3 - 2 \sqrt{2} )}^{3} \\ 9 - 16 \sqrt{2} - 18 \sqrt{2} (3 - 2 \sqrt{2} ) \\ {x}^{3} = 9 - 16 \sqrt{2} - 48 \sqrt{2} + 36 \sqrt{2} \\ {x}^{3} = 9 - 28 \sqrt{2} \\ \frac{1}{ {x}^{3} } = \frac{1}{9 - 28 \sqrt{2} } \\ {x}^{3} + \frac{1}{ {x}^{3} } = 9 - 28 \sqrt{2} + \frac{1}{9 - 2 8\sqrt{2} } \\ = \frac{81 + 1568 - 504 \sqrt{2} + 1 }{9 - 28 \sqrt{2} } \\ \frac{1645 - 504 \sqrt{2} }{9 - 28 \sqrt{2} }$