Question

The sum of a number 28 times it's reciprocal is 16. Fine the number.

Answer 1

The solution to the problem is x = 2.

Let's denote the number as x. According to the given information, we can set up the equation:

`\[x + 28\left((1)/(x)\right) = 16\]`

To solve for x, we can first multiply through by x to get rid of the fraction:

`\[x^2 + 28 = 16x\]`

Now, we rearrange the equation to form a quadratic equation:

`\[x^2 - 16x + 28 = 0\]`

To solve for x, we can use the quadratic formula:

`\[x = (-b \pm √(b^2 - 4ac))/(2a)\]`

In this case, a = 1, b = -16, and c = 28. Plugging these values into the quadratic formula gives two potential solutions for x.

However, it's important to check whether these solutions satisfy the original equation since we might end up with extraneous solutions.

After solving, we find two potential solutions:
`\(x = 2\) and \(x = 14\)`. We can verify that x = 2 is the correct solution:

`\[2 + 28\left((1)/(2)\right) = 2 + 14 = 16\]`