Question

if x=2+under root 3 find the value of x^3+1/x^3

Answer 1

Step-by-step explanation:

$x = 2 + \sqrt{3} \\ \frac{1}{x} = 2 - \sqrt{3} \\ now \: \: x + \frac{1}{x} = 4 \\ {x}^{3} + \frac{1}{ {x}^{3} } \\ = {(x + \frac{1}{x} )}^{3} - 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) \\ = {4}^{3} - 3 \times 4 \\ = 64 - 12 \\ = 52$

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