Question

The sum of a number and its reciprocal is 17/4. What is the number?

Answer 1

Solution is number is `4` or `1/4`.

Explanation:

Let the be `x`. Then, its reciprocal is `1/x`.

Therefore we have `x+1/x=17/4`

Multiplying every term by `4x`, we get

`4x xx x+4x xx 1/x=4x xx17/4`

i.e. `4x xx x+4cancelx xx 1/cancelx=cancel4x xx17/cancel4`

or `4x^2+4=17x`

or `4x^2-17x+4=0`

or `4x^2-16x-x+4=0`

or `4x(x-4)-1(x-4)=0`

or `(4x-1)(x-4)=0`

i.e. either `4x-1-0` i.e. `4x=1` and `x=1/4`

or `x-4=0` and `x=4`

Hence, solution is number is `4` or `1/4`.

This is so because not only both of them add up to `17/4`, but also that each is reciprocal of the other one.