Question

if x= root 5 -2, find the value of (x-1/x )^3

Answer 1

Answer:

$\frac{32\sqrt{5} + 72}{17\sqrt{5} + 38}$

Step-by-step explanation:

$x = \sqrt{5} - 2$

Substituting value of x in $(\frac{x - 1}{x}) ^{3}$

$(\frac{\sqrt{5} - 2 - 1 }{\sqrt{5} - 2 }) ^{3}$

= $(\frac{\sqrt{5} - 3 }{\sqrt{5} - 2 }) ^{3}$

= $\frac{(\sqrt{5} - 3) ^{3} }{(\sqrt{5} - 2)^{3} }$

= $\frac{(\sqrt{5}) ^{3} - (-3)^{3} - 3(\sqrt{5})(-3)(\sqrt{5} + 3) }{(\sqrt{5}) ^{3} - (-2)^{3} - 3(\sqrt{5})(-2)(\sqrt{5} + 2)}$

= $\frac{5\sqrt{5} - (-27) + 9\sqrt{5}(\sqrt{5} + 3)}{5\sqrt{5} - (-8) + 6\sqrt{5}(\sqrt{5} + 2)}$

= $\frac{5\sqrt{5} + 27 + 45 + 27\sqrt{5}}{5\sqrt{5} + 8 + 30 + 12\sqrt{5}}$

= $\frac{32\sqrt{5} + 72}{17\sqrt{5} + 38}$  

Hope it helped!!!

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