Math, asked by mishraanya63, 8 months ago

if x=2+√3
.
.
then
x^3+1/(x)^3​

Answers

Answered by mathdude500
2

Answer:

x = 2 +  \sqrt{3}  \\  \frac{1}{x}  =  \frac{1}{2 +  \sqrt{3} }  \times  \frac{2 -  \sqrt{3} }{2 -  \sqrt{3} }  =   \frac{2 -  \sqrt{3} }{ {2}^{2}  -  {( \sqrt{3} )}^{2} }  = 2 -  \sqrt{3}  \\ so \:  {x}^{3}  +  \frac{1}{ {x}^{3} }  =  {(2 +  \sqrt{3}) }^{3}  +  {(2 -  \sqrt{3} )}^{3}  \\  = 2( {(2)}^{3}  + 3(2){ (\sqrt{3} )}^{2} ) \\  = 2(8 + 18) \\  = 2 \times 26 \\  = 52

Answered by suman8615
0

Answer:

answer is 52...............

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