Question

if x^2/x+1/x=5/2 find the value of (i) x-1/x (ii) x^3-1/x^3


pls answer fast

Answer 1

Here , we have the Information given as -

$\sf{ \dfrac{ x^2 }{ x } + \dfrac{ 1}{ x } = 52 } \\ \\ \sf{ This \: can \: be \: written \: as \: - } \\ \\ \sf{ x + \dfrac{1}{x} = 52 } \\ \\ \sf{ \bold { Squaring \: - }} \\ \\ \sf{ \implies { x ^ 2 + \dfrac{1}{x^2} + 2 = 2704 }} \\ \\ \sf{ \implies { x ^ 2 + \dfrac{1}{x^2 } - 2 = 2700 } } \\ \\ \sf{ \bold { Taking \: Square \: root \: - } } \\ \\ \sf{ \implies { x - \dfrac{ 1 }{ x } \approx 52 }} \\ \\ \sf{ Cubing \: This \: - } \\ \\ \sf{ \implies { x ^ 3 - \dfrac{1}{ x ^ 3 } - 3 \times 52 = 140608 }} \\ \\ \sf{ \implies { x ^ 3 - \dfrac{ 1 }{ x ^ 3 } = 140608 + 156 }} \\ \\ \sf{ \implies { x ^ 3 - \dfrac{ 1 }{ x ^ 3 } = 140764 }} \\ \\ \sf{ \bold { This \: Is \: The \: required \: answer \: . }}$

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