Question

if x+1/x = 4 find x4 - 1/x3

Answer 1

SOLUTION

$\frac{x + 1 }{4 } = 4\\ \\ x + 1 = 4x \\\\ x - 4x = -1\\ \\ -3x = -1 \ OR \ 3x = 1 \\\\ x = \frac{1}{3}$

Now we have to find the value of  

$x^{4} - \frac{1}{x^{3}} \\\\ Putting \ the \ value \ of \ x = \frac{1}{3} \\\\ x^{4} - \frac{1}{x^{3}} = (\frac{1}{3} )^{\frac{1}{3}} - \frac{1}{(\frac{1}{3})^{3}} \\\\ (\frac{1}{3} )^{\frac{1}{3}} - 3^3 \ .................................... ( \frac{1}{(\frac{1}{3})^{3}} = 3^3 ) \\\\ \frac{1}{81} - 27 \\\\ - \frac{2186}{81} \ or \ - 26 \frac{80}{81} \ ............................ \ Ans$

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