Question

If x+1/x=6
then x^3-(1/3)^3=?


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Answer 1

Answer:

198

Step-by-step explanation:

$\displaystyle6^3 = \bigl(x+\tfrac1x\bigr)^3\\\\=x^3+3x^2\tfrac1x + 3x\tfrac1{x^2} + \tfrac1{x^3}\\\\=\bigl(x^3+\tfrac1{x^3}\bigr) + 3\bigl(x+\tfrac1x\bigr)\\\\=\bigl(x^3+\tfrac1{x^3}\bigr) + (3)(6)\\\\\Rightarrow x^3+\tfrac1{x^3}= 6^3-(3)(6) = 6(6^2-3)=6\times33=18\times11=198$