Question

If x = 3+2root2 find value of x^3 - 1/x^3

Answer 1

Answer:

140$\sqrt{2}$

Step-by-step explanation:

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

(x - 1/x)^3 = x^3 - (1/x)^3 + 3/x - 3x

= x^3 - 1/x^3 - 3(x - 1/x)

=> x^3 - 1/x^3 = (x - 1/x)^3 + 3(x - 1/x)

x - 1/x = $3 + 2\sqrt{2}$ - $\frac{1}{3 + 2\sqrt{2} }$

= $3 + 2\sqrt{2} - \frac{3 - 2\sqrt{2}}{1}$

= $3 - 3 + 2\sqrt{2} + 2\sqrt{2}$

= $4\sqrt{2}$

(x - 1/x)^3 = 128$\sqrt{2}$

x^3 - 1/x^3 = 128$\sqrt{2}$ + 3(x - 1/x)

= 128$\sqrt{2}$ + 3(4$\sqrt{2}$)

= 140$\sqrt{2}$

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