Fraction and Decimal: Reciprocal of x's non-integerThe reciprocal part of x's non-integer decimal part equals x + 1, and x &gt; 0. What is x?Solution: I tried this way-Let's n= integer part of x 1 / x − n = x + 1or, 1 = ( x − n ) ( x + 1 )or, 1 = x 2 + x − n x − nor, x 2 + ( 1 − n ) x − ( n + 1 ) = 0but, stucked here. Is there any other way?

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Fraction and Decimal: Reciprocal of x&#039;s non-integerThe reciprocal part of   x&#039;s non-integer decimal part equals   x  +  1, and   x  &amp;gt;  0. What is   x?Solution: I tried this way-Let&#039;s   n= integer part of   x  1      /    x  −  n  =  x  +  1or,   1  =  (  x  −  n  )  (  x  +  1  )or,   1  =      x    2    +  x  −  n  x  −  nor,       x    2    +  (  1  −  n  )  x  −  (  n  +  1  )  =  0but, stucked here. Is there any other way?

Esteban Johnson · Accepted Answer

To complete Ashvin Swaminathan&#039;s answer:  x  =            n      −      1      ±                        n          2                +        2        n        +        5              2  Because   x  &amp;gt;  0, we take  x  =            n      −      1      +                        n          2                +        2        n        +        5              2  Since the discriminant       n    2    +  2  n  +  5  =  (  n  +  1      )    2    +  4  ≥  4, then there are indeed infinitely many solutions, and these depend on   n  =  ⌊      x    ⌋

landdenaw · Accepted Answer

Solve for   x using the quadratic formula. As stated, there are infinitely many solutions...

Fraction and Decimal: Reciprocal of x's non-integer The reciprocal part of x 's non-integer d

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