Question

14. X=2+ V3.find the value of x +
X^3+1/x^3​

Answer 1

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

Answer 2

Step-by-step explanation:

$\begin{gathered}x = 2 + \sqrt{3} \\ \frac{1}{x} = 2 - \sqrt{3} \\ (by \: rationalizing \: demoinator) \\ now \: \: \: {x}^{3} + \frac{1}{ {x}^{3} } = ( {x + \frac{1}{x} })^{3} - 3(x + \frac{1}{x} ) \\ = {4}^{3} - 3 \times 4 \\ = 64 - 12 \\ = 52\end{gathered}x=2+3x1=2−3(byrationalizingdenominator)nowx3+x31=(x+x1)3−3(x+x1)=43−3×4=64−12=52</p><p>$