Math, asked by sd9136209, 2 months ago

if x= 2-√3, find the value of (x- 1/x ) ^3​

Answers

Answered by Vincent2021
0

x=2-√3

=>1/x = 1/(2-√3)

=>1/x=2+√3

Now,

x-(1/x)=(2-√3)-(2+√3)

=>x-(1/x)=-2√3

=>{x-(1/x)} ³=-24√3

Answered by rkcomp31
1

Answer:

Step-by-step explanation:

x= 2-\sqrt{3} \\\\\frac1x=\frac{1}{2-\sqrt{3}} =\frac{2+\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})} \\\\\bf \frac1x=\frac{(2+\sqrt{3})}{4-3} =2+\sqrt{3}

Now

(x-\frac1x)^3=[2-\sqrt{3}-(2+\sqrt{3})]^3\\\\=(-2\sqrt{3} )^3\\\\=(-2)^3(\sqrt{3} )^3\\\\=-8\times 3\sqrt{3} \\\\\bf=-24\sqrt{3}

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