The sum of twice a number and thrice its reciprocal is 25/2. What is the number?

The sum of twice a number and thrice its reciprocal is 25/2. What is the number?
1). 7
2). 6
3). 5
4). 4

Let the number be x.

The given equation is:
2x + 3/x = 25/2

Multiply both sides by 2x to remove the fraction:
4x² + 6 = 25x

Rearrange:
4x² - 25x + 6 = 0

Solve using the quadratic formula:
x = (25 ± √529) / 8
x = (25 ± 23) / 8

The possible values are:
x = 6 or x = 1/4

Since 6 is in the given options, the answer is 6.

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