x3 +1/x3=52 find x+1/x
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Answered by
125
x³ + 1/x³ = 52
(x + 1/x)³ -3(x + 1/x ) = 52
let ( x + 1/x ) = t
t³ -3 t -52 = 0
t³ -4t² + 4t² -16t +13t -52 = 0
t²( t -4) +4t( t -4) +13( t -4) = 0
( t -4) ( t² +4t +13) = 0
t = 4 and t² + 4t +13 have no real value so,
x + 1/x = 4
(x + 1/x)³ -3(x + 1/x ) = 52
let ( x + 1/x ) = t
t³ -3 t -52 = 0
t³ -4t² + 4t² -16t +13t -52 = 0
t²( t -4) +4t( t -4) +13( t -4) = 0
( t -4) ( t² +4t +13) = 0
t = 4 and t² + 4t +13 have no real value so,
x + 1/x = 4
Answered by
8
Answer:
x³ + 1/x³ = 52
(x + 1/x)³ -3(x + 1/x ) = 52
let ( x + 1/x ) = t
t³ -3 t -52 = 0
t³ -4t² + 4t² -16t +13t -52 = 0
t²( t -4) +4t( t -4) +13( t -4) = 0
( t -4) ( t² +4t +13) = 0
t = 4 and t² + 4t +13 have no real value so,
x + 1/x = 4
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