If 2x + (2/x) = 3, then the value of x³ + (1/x³) + 2 is:
2018
If 2x + (2/x) = 3, then the value of x³ + (1/x³) + 2 is:
- A.
3/8
- B.
19/8
- C.
21/8
- D.
7/8
Attempted by 41 students.
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Correct answer: D
Given: 2x + (2/x) = 3.
Divide both sides by 2: x + (1/x) = 3/2.
Use the identity (x + 1/x)³ = x³ + 1/x³ + 3(x + 1/x).
Rearranging: x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x) = (3/2)³ - 3(3/2).
Since (3/2)³ = 27/8 and 3(3/2) = 9/2 = 36/8, we get x³ + 1/x³ = 27/8 - 36/8 = -9/8.
Finally add 2: x³ + 1/x³ + 2 = -9/8 + 16/8 = 7/8.
Therefore the required value is 7/8.