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