The difference of a integers and it's reciprocal is 143/2 . Find the integers
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Let the integer be x
Its reciprocal be 1/x
Given :
x - 1/x =143/12
[Taking LCM]
(x×x -1)/x = 143/12
(x²-1)/x = 143/12
12(x²-1) = 143 × x
12x²-12= 143x
12 x² -143x-12=0
[ Add & Subtract x]
12x²-143x -x+x-12=0
12x²-144x +x-12= 0
12x(x -12) +1(x-12)= 0
(x-12)(12x+1)=0
x=12, 12x= -1, x= -1/12
x= 12, x= -1/12
Since x is an integer, hence x=12
Its reciprocal be 1/x
Given :
x - 1/x =143/12
[Taking LCM]
(x×x -1)/x = 143/12
(x²-1)/x = 143/12
12(x²-1) = 143 × x
12x²-12= 143x
12 x² -143x-12=0
[ Add & Subtract x]
12x²-143x -x+x-12=0
12x²-144x +x-12= 0
12x(x -12) +1(x-12)= 0
(x-12)(12x+1)=0
x=12, 12x= -1, x= -1/12
x= 12, x= -1/12
Since x is an integer, hence x=12
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