Question

if x+1/x=5,determine x^3+1/x^3.​

Answer 1

As we know,

⇒ (x + 1/x)2 = x2 + 1/x2 + 2

Given, x + 1/x = 5

⇒ (x + 1/x)3 = x3 + 1/x3 + 3 (x + 1/x)

⇒ 53 = x3 + 1/x3 + 3 × 5

⇒ x3 + 1/x3 = 125 – 15 = 110

Answer 2

$x + \frac{1}{x} = 5$

${x}^{3} + \frac{1}{ {x}^{3} } = \: ?$

$( {a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)$

$(x + \frac{1}{x} ) ^{3} = {5}^{3}$

${x}^{3} + \frac{1}{ {x}^{3} } + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 125$

${x}^{3} + \frac{1}{ {x}^{3} } + 15 = 125$

${x}^{3} + \frac{1}{ {x}^{3} } = 125 - 15$

${x}^{3} + \frac{1}{ {x}^{3} } = 110$