Question

if x = 2-root3,find the value of ( x-1/x)power3​

Answer 1

$x = 2 - \sqrt{3}$

$1 \div x = 1 \div 2 - \sqrt{3}$

$1 \div x = 1 \div 2 - \sqrt{3 } \times 2 + \sqrt{3} \div 2 + \sqrt{3}$

$1 \div x = 2 + \sqrt{3} \div 1$

$substiting \: x \: and \: 1 \div x$

$(2 - \sqrt{3} \times 2 + \sqrt{3 } \div 1) {}^{3}$

$(a - b)(a + b) = a {}^{2} - b {}^{2}$

$(2 {}^{2} + (\sqrt{3} ) {}^{2} ) {}^{3}$

$(4 - 3) {}^{3}$

$(1) {}^{3}$

$= 1$