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