If x³ + 1/x³ =110, then x +1/x = ?
A. 5
B. 10
C. 15
D. none of these
Answers
Given : x³ + 1/x³ = 110
By using an algebraic identity :
(a + b)³ = a³ + b³ + 3 ab (a + b)
We have :
(x + 1/x)³ = x³ + 1/x³ + 3 x × 1/x (x + 1/x)
(x + 1/x)³ = 110 + 3 (x + 1/x)
(x + 1/x)³ - 3 (x + 1/x) - 110 = 0
Let x + 1/x = a
a³ - 3a = 110
Taking a as a common :
a(a² - 3) = 110
a(a² - 3) = 5(5² - 3)
On comparing :
a = 5
Then , x + 1/x = a
x + 1/x = 5
Hence , x + 1/x is 5
Option (A) 5 is correct.
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Answer:
Step-by-step explanation:
(x + 1/x)³ = x³ + 1/x³ + 3 x × 1/x (x + 1/x)
(x + 1/x)³ = 110 + 3 (x + 1/x)
(x + 1/x)³ - 3 (x + 1/x) - 110 = 0
Let x + 1/x = a
a³ - 3a = 110
Taking a as a common :
a(a² - 3) = 110
a(a² - 3) = 5(5² - 3)
On comparing :
a = 5
Then , x + 1/x = a
x + 1/x = 5