Question

The difference of an integer and its reciprocal is 143 12
. Find the
integer

Answer 1

Step-by-step explanation:

Let the integer be x

Its reciprocal is 1/x

x-1/x=143/12

(x²-1)/x=143/12

12(x²-1)=143x

12x²-12=143x

12x²-143x-12=0

12x²-144x+x-12=0

12x(x-12)+1(x-12)=0

(12x+1)(x-12)=0

x=12 or -1/12

x is an integer, not a rational number

So x=12

Answer 2

Answer:

12

Step-by-step explanation:

Let x be an integer and its reciprocal 1/x

Difference x− 1/x= 143/12⇒12(x^2 -1)= 143x

⇒12x^2 −143 x−12=0

⇒12x^2 −144x+x−12=0

⇒12x(x−12)+1(x−12)=0

∴x= -1/12 ,12

Hence x=12 is the only solution (since x∈I)