Question

If x- ¹/x=15 find x³-¹/x³

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Answer 1

Answer:

As we see that the x has a power of 3 so we begin by cubbing the whole equation.

So we start solving like:

[math]x + \dfrac{1}{x} = 3[/math]

[math](x + \dfrac{1}{x})^3 = 3^3[/math]

[math]x^3 + 3.x^2.\dfrac{1}{x} + 3.x.\dfrac{1}{x^2} + \dfrac{1}{x^3} = 27[/math]

[math](x^3 + \dfrac{1}{x^3}) + 3.x^2.\dfrac{1}{x} + 3.x.\dfrac{1}{x^2} = 27[/math]

[math]x^3 + \dfrac{1}{x^3} + (3x + \dfrac{3}{x}) = 27[/math]

[math]x^3 + \dfrac{1}{x^3} + 3(x + \dfrac{1}{x}) = 27[/math]

[math]x^3 + \dfrac{1}{x^3} + 3 × 3 = 27[/math]

[math]x^3 + \dfrac{1}{x^3} + 9 = 27[/math]

[math]x^3 + \dfrac{1}{x^3} = 18[/math]

Therefore the answer is 18