Question

if x=2+√3 find the value of x^3+1/x^3​

Answer 1

Answer:

52

Step-by-step explanation:

Given, x = 2 + $\sqrt{3}$

$\frac{1}{x}$ = $\frac{1}{2+\sqrt{3}}$ = 2 - $\sqrt{3}$                        ...(rationalizing the denominator)

[x + $\frac{1}{x}$]³ = x³ + $\frac{1}{x^{3}}$ + 3(x + $\frac{1}{x}$)

= [2 + $\sqrt{3}$ + 2 - $\sqrt{3}$]³ - 3(2 + $\sqrt{3}$ + 2 - $\sqrt{3}$) = x³ + $\frac{1}{x^{3}}$

= 4³ - 12 = x³ + $\frac{1}{x^{3}}$

= 64 -12 = x³ + $\frac{1}{x^{3}}$ = 52

Note:

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