Answer:
110
Step-by-step explanation:
Using the expansion
(a + b)³ = a³ + b³ + 3ab(a + b)
Given
x + [tex]\frac{1}{x}[/tex] = 5 ( cube both sides )
(x + [tex]\frac{1}{x}[/tex] )³ = 5³ = 125 ← expand left side using identity
x³ + [tex]\frac{1}{x^3}[/tex] + 3(x × [tex]\frac{1}{x}[/tex] )(x + [tex]\frac{1}{x}[/tex] ) = 125
x³ + [tex]\frac{1}{x^3}[/tex] + 3(1)(5) = 125
x³ + [tex]\frac{1}{x^3}[/tex] + 15 = 125 ( subtract 15 from both sides )
x³ + [tex]\frac{1}{x^3}[/tex] = 110
