Question

The additive inverse of a number divided by 12 is the same as one less then Three times its Reciprocal. Find the number

Answer 1

Let the number be a

Additive inverse = - a

Reciprocal = 1/a

According to question,

3 × Reciprocal - Additive inverse/ 12 = 1

3/a - (-a)/ 12= 1

=> 3/a + a /12 = 1

=> ( 36+ a^2) / 12a = 1

=> a^2 + 36 = 12a

=> a^2 - 12a + 36 = 0

=> a^2 - 6a - 6a + 36 = 0

=> a(a - 6) - 6(a - 6) = 0

=> (a - 6)(a - 6) = 0

=> (a-6)^2 = 0

=> a - 6 = 0

=> a = 6

Required number = 6