Question

$If \: x = \frac{1}{8 - \sqrt{60} }$
$what \: is \: the \: value \: of \: ( {x}^{3} - {5}^{2} + 8x - 4)?\ \textless \ br /\ \textgreater$
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Answer 1

Answer:

$\left(\frac{1}{8-\sqrt{60}}\right)^3-5^2+8\times \frac{1}{8-\sqrt{60}}-4=-\left(-\frac{95\sqrt{15}+372}{8}\right)-29$

Step-by-step explanation:

$\left(\frac{1}{8-\sqrt{60}}\right)^3-5^2+8\times \frac{1}{8-\sqrt{60}}-4$

$=\frac{1}{1952-504\sqrt{15}}-5^2+\frac{4}{4-\sqrt{15}}-4$

$=\frac{4}{4-\sqrt{15}}+\frac{1}{1952-504\sqrt{15}}-5^2-4$

$=-5^2-\frac{7812-2017\sqrt{15}}{3968\sqrt{15}-15368}-4$

$5^2=25$

$=-25-\frac{7812-2017\sqrt{15}}{3968\sqrt{15}-15368}-4$

$\mathrm{Subtract\:the\:numbers:}\:-25-4=-29$

$=-\frac{7812-2017\sqrt{15}}{3968\sqrt{15}-15368}-29$

$=-\left(-\frac{95\sqrt{15}+372}{8}\right)-29$