# The additive inverse of a number, divided by twelve is the same as one less than three times its reciprocal. Find the number

2
by charlotteds9

2016-04-28T10:41:26+05:30
Let the number be x. And it's additive inverse will be -x. Now dividing it by 12 that is -x/12. Now one less than three times it reciprocal is 3/x -1. As they both are equal X/12 = 1 - 3/x. X/12 = x -3/x. X^2 = 12x - 36. X^2 - 12x + 36 = 0. Therefore ( x -6 )^2 = 0. And hence x - 6 = 0. And x = 0
how can be x = 0
And hence x - 6 = 0. And x = 0 .........is this correct?
No that x = o has come by mistake...x = 6 only
2016-04-28T12:50:30+05:30

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Let the required number = x
according to the question,
additive inverse of the  number = -x
condition : -x/12 = 3/x -1
-x/12 = (3-x)/ x
- x²    = 36 - 12x
x² - 12x +36 = 0
x ² -6x- 6x + 36 =0
x(x - 6) - 6( x - 6) = 0
(x-6)(x-6) = 0
x = 6
therefore , the number is 6.