SOLUTION: I am not sure how to do the problem which I will write down. I hope you can help me. Thank you in advance. The sum of a number and its reciprocal is 17/4. Find the number.

Algebra ->  Customizable Word Problem Solvers  -> Unit conversion -> SOLUTION: I am not sure how to do the problem which I will write down. I hope you can help me. Thank you in advance. The sum of a number and its reciprocal is 17/4. Find the number.       Log On

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Question 1134880: I am not sure how to do the problem which I will write down. I hope you can help me. Thank you in advance.
The sum of a number and its reciprocal is 17/4. Find the number.
Found 3 solutions by josgarithmetic, ikleyn, Theo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and 1/x.

x%2B1%2Fx=17%2F4
4x%28x%2B1%2Fx%29=4x%2817%2F4%29
4x%5E2%2B4=17x
4x%5E2-17x%2B4=0
Can you solve it now?

Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
The problem asks you to find the number x based on this equation, which follows directly from the description


    x + 1%2Fx = 17%2F4.


To solve it, multiply both sides by 4x. You will get


    4x^2 + 4 = 17x,   or, equivalently,


    4x^2 - 17x + 4 = 0.


Next step is to solve this quadratic equation. You can do it using the quadratic formula


    x%5B1%2C2%5D = %2817+%2B-+sqrt%2817%5E2+-+4%2A4%2A4%29%29%2F%282%2A4%29 = %2817+%2B-+15%29%2F8.


So, the problem has two solutions


    x%5B1%5D = %2817+%2B+15%29%2F8 = 32%2F8 = 4,   and

    x%5B2%5D = %2817+-+15%29%2F8 = 2%2F8 = 1%2F4.

Solved.


Do not forget to post your "Thanks" to me for my help ! !



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let the number be x.

it's reciprocal would then be 1/x

you are given that the sum of the number and its reciprocal is equal to 17/4.

that means that x + 1/x = 17/4

place the expression on the left side of this equation under a common denominator and the equation becomes:

(x^2 + 1) / x = 17 / 4

cross multiply to get (x^2 + 1) * 4 = x * 17

simplify to get 4 * x^2 + 4 = 17 * x

subtract 17 * x from both sides of the equation to get 4 * x^2 - 17 * x + 4 = 0

factor this equation to get (4x-1) * (x-4) = 0

solve for x to get x = 1/4 or x = 4.

if you let x = 4, then its reciprocal is 1/4 and 4 + 1/4 is equal to 17/4.

if you let x = 1/4, then its reciprocal is 4 and 1/4 + 4 = 17/4.

the number can either be 4 or 1/4.

either one will get you the correct answer.