Question

if x = 2 - root 3.
Find the value of (x-1/x) ^3
​

Answer 1

$We \:have \: x = 2 - \sqrt{3}\: ---(1)$

$i ) \frac{1}{x} = \frac{1}{(2 - \sqrt{3})}$

$= \frac{(2+\sqrt{3})}{ (2 - \sqrt{3})(2 +\sqrt{3})} \\= \frac{(2+\sqrt{3})}{ 2^{2} - \sqrt{3}^{2}} \\= </p><p>\frac{(2+\sqrt{3})}{ 4- 3} \\= \frac{(2+\sqrt{3})}{ 1} \\= 2+ \sqrt{3} \: --(2)$

$ii ) x - \frac{1}{x} \\= 2- \sqrt{3} -( 2+ \sqrt{3})\\= 2- \sqrt{3} - 2- \sqrt{3}\\= -2\sqrt{3} \: ---(3)$

$iii ) Now,\red{ Value \:of \: \Big(x - \frac{1}{x}\Big)^{3} }\\= (-2\sqrt{3})^{3} \\= - 8 \times 3 \sqrt{3}\\= -24\sqrt{3}$

Therefore.,

$\red{ Value \:of \: \Big(x - \frac{1}{x}\Big)^{3} }\green {=-24\sqrt{3}}$

•••♪