1.

The sum of q number and it's reciprocal is 3, find the number​

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Answer:

Reciprocal means 1 DIVIDED by that number. For example, the reciprocal of 2 is 1/2.

So lets call the number we are trying to find x.

x + 1/x = 3

so, now rearrange x and 1/x so they have the same denominator (the bottom part of the fraction). To do this, we can say that x = x/1. TIMES the top and bottom by x. That gives x2/x.

so...

x2/x + 1/x = 3

now we can add the fractions.

(x2+1) / x = 3

Times each side of the equation by x.

x2+1 = 3x

x2 -3x +1 = 0

This is a quadratic equation that we can solve, to find x.

Then you can use the quadratic formula to find x. If you want to see how this works, go to:

but it gives us the answers:

x =  (3+sqrt5)/2

or   (3-sqrt5)/2

(sqrt 5 means the square root of 5)

which come out as 2.618 (to 3 decimal places)

and 0.382 (to 3 decimal places)

and you can check: when you add them to their reciprocal, you get 3


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