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(x+1/x)^3- 3(x+1/x) |
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Answer» ONG>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 |
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