Question

the additive inverse of a number divided by 12 is the same as one less than three times its reciprocal. find the number

Answer 1

let the number =A,

then

additive inverse of number=-A,

reciprocal of the number=1/A,

According to question, we have

-A/12 = 3/A-1,

then
1 = 3/A + A/12,

1 = (36+A²)/12A,

12A=36+A²,

then

A²-12A+36=0,

A²-(6+6)A+36=0,

A²-6A-6A+36=0,

A(A-6)-6(A-6)=0,

(A-6)(A-6)=0,

then

A=6

Answer 2

$\underline{\large{\text{Answer :}}}$

Let, the number be x, which is non - zero

Then, its additive inverse is (-x) and its reciprocal is $\frac{1}{x}$

By the given condition,

$\frac{ - x}{12} = \frac{3}{x} - 1 \\ \\ \to \frac{ - x}{12} = \frac{3 - x}{x} \\ \\ \to - {x}^{2} = 36 - 12x \\ \\ \to {x}^{2} - 12x + 36 = 0 \\ \\ \to (x - 6)(x - 6) = 0 \\ \\ \therefore x = 6,6$

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