Question

X^3 +1/x^3=110
Find x+1/x=??

Answer 1

Question :

• ➽ x³ + 1/x³ = 110

Find :

• ➽ x + 1/x

Solution :

• ➣ (x + 1/x)³ = (x³ + 1/x³) + 3 (x + 1/x)

• ➣ (x + 1/x)³ = 110 + 3 (x + 1/x)

Let y = x + 1/x

➝ y³ = 110 + 3y

➝ y³ − 3y − 110 = 0

➝ y³ − 5y² + 5y² − 3y − 110 = 0

➝ y² (y − 5) + 5y² −25y + 22y − 110 = 0

➝ y² (y − 5) + 5y (y − 5) + 22 (y − 5) = 0

➝ (y − 5)(y² + 5y + 22) = 0

➝ y = 0 or y = −5 ± 3√7i/2

❍Therefore,

• Hence, the value of x + 1/x is 5.

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