If x-1/x=5 , then x^3-1/x^3 = 1) 1002) 1253) 1404) 145

1.	If x-1/x=5 , then x^3-1/x^3 = 1) 1002) 1253) 1404) 145
Answer» ANSWER: → 140 ★ GivEn :- $\sf \: x - \dfrac{1}{x} = 5$ ★ To Find :- $\sf \: value \: of \: {x}^{3} - \dfrac{1}{ {x}^{3} }$ Step-by-step explanation: $\sf \: x - \dfrac{1}{x} = 5$ $\implies \: \sf \: (x - \dfrac{1}{x})^{2} = {5}^{2}$ (By squaring both SIDES..) $\implies \sf \: {x}^{2} + \dfrac{1}{ {x}^{2} } - 2 \times x \times \dfrac{1}{x} = 25$ $\implies \sf \: {x}^{2} + \dfrac{1}{ {x}^{2} } - 2 = 25$ $\implies \sf \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 25 + 2$ $\implies \sf \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 27$ Now, $\sf \: {x}^{3} - \dfrac{1}{ {x}^{3} }$ $\implies \sf \: (x - \dfrac{1}{x} )( {x}^{2} + \dfrac{1}{ {x}^{2} } + x \times \dfrac{1}{x} )$ (PUTTING the VALUES) $\implies \sf \: 5 \times (27 + 1)$ $\implies \sf \: 5 \times 28$ $\implies \boxed{ \red{\sf \: {x}^{3} - \dfrac{1}{ {x}^{3} } = 140}}$

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→ 140

★ GivEn :-