Question

the additive inverse of a number divided by twelve is the same as one less then three times its reciprocal.find the number

Answer 1

Let the number be x.
We know that,
Additive inverse of this number = -x
Reciprocal = 1/x .

According to the question,
-x/12 = 3/x - 1

-x/12 = 3 - x / x

-x² = 12 ( 3 - x)

-x² = 36 - 12x

x² - 12x + 36 = 0

x² - 6x - 6x + 36 = 0

x ( x - 6 ) -6 ( x - 6 ) = 0

( x - 6 ) = 0

x = 6 .


Therefore, The number is 6 .

Answer 2

Hello user☺☺

Let the number be x

So, the additive inverse will be -x

Now, A.T.Q. , we have

-x/12 = 3/x - 1

x/12 + 3/x = 1

x^2 + 36 = 12x

x^2 -12x + 36 = 0

(x-6)^2 = 0

(x-6) = 0

x = 6.

So, the number will be 6.

Hope this will help☺☺