Question

If x + 1/x = 3, then the value of x2 +c^3 is equal to​

Answer 1

Answer:

(109+5√13) /54

Step-by-step explanation:

x+1/x = 3

=> (x²+1)/x = 3

=> x²+1 = 3x

=> x²+1-3x = 0

=> x = {-1±√(1+12)}/2 [ by sridharacharya formula ]

=> x = {-1±√13}/2

x² = {-1+√13}²/2²

= (-1²+√13²+2×-1×√13) /4

= (1+13-2√13)/4

= (14-2√13)/4

= (7-√13)/2 -------(1)

x³ = {-1+√13}³/3³

= (-1³+√13³+3×-1²×√13+3×-1×√13²) /27

= (-1+13√13+3√13-39) /27

= (16√13-40)/27 --------(2)

adding (1) + (2)

(7-√13)/2 + (16√13-40)/27

= (189-27√13+32√13-80) /54

= (109+5√13)/54

actual value calculated is 2.35236586 (approximately)

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