SOLUTION: When a number is decreased by its reciprocal, the result is 2 1/10

Question 1061283: When a number is decreased by its reciprocal, the result is 2 1/10
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x be the number.

you get x - 1/x = 21/10

multiply both sides of this equation by 10x to get:

10x^2 - 10 = 21x

subtract 21x from both sides of the equation to get:

10x^2 - 21x - 10 = 0

solve this quadratic equation to get:

x = -.4 or x = 2.5

replace x in the original equation with each of these values and you will see that both values are valid.

your solution is that the number will either be 2.5 or -.4.

however, when x = -.4 and you subtract it's reciprocal, you get 2.1 which is larger than -.4, so, even though you subtracted it's reciprocal from it, you wound up with a larger number, which may not be considered a decrease.

that leaves you with 2.5 as your number.

the answer could be either but, if you need just one number, i would go with 2.5.

it all comes down to determining what they mean by decrease.

technically, when you decrease a number by something, you are subtracting that something from it, but this gets topsy turvy when you are dealing with negative numbers, because when you subtract a negative number, you are effectively adding a positive number, which is an increase.

if i had to guess what they're looking for, i would guess that they're looking for 2.5 as the answer.

but i could be wrong, depending on what they're really looking for.

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