Question

if x+1/x=5 ,find value 0f x^3+1/x^3​

Answer 1

(x + 1/x)³  = x³ + 1/x³ + 3x²*1/x + 3x*1/x² = x³ + 1/x³ + 3x + 3/x

ie, (x + 1/x)³ = x³ + 1/x³ +3 (x + 1/x)

now, substitute the values we have.

ie, 5³ = x³ + 1/x³ + 3*5

x³ + 1/x³ = 125 - 15 = 110

Answer 2

$x \: + \: \dfrac{1}{x} \: = \: 5$

____________ [GIVEN]

• We have to find the value of ${x}^{3} \: + \: \dfrac{1}{ {x}^{3}}$

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$x \: + \: \dfrac{1}{x} \: = \: 5$

Take cube on both sides

=> $\bigg( {x \: + \: \dfrac{1}{x} \bigg )}^{3} \: = \: (5)^{3}$

(a + b)³ = a³ + b³ + 3ab (a + b)

=> ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} } \: + \: 3x \: \times \: \dfrac{1}{x} \: \bigg(x \: + \: \dfrac{1}{x} \bigg) \: = \: 125$

=> ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} } \: + \: 3\: (5) \: = \: 125$

=> ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} } \: + \: 15\: = \: 125$

=> ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} } \: = \: 125\:-\:15$

=> ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} } \: = \: 110$

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${x}^{3} \: + \: \dfrac{1}{ {x}^{3} } \: = \: 110$

________ [ANSWER]

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