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

Lovellss 2022-06-25 Answered
Fraction and Decimal: Reciprocal of x's non-integer
The reciprocal part of x's non-integer decimal part equals x + 1, and x > 0. What is x?
Solution: I tried this way-
Let's n= integer part of x
1 / x n = x + 1
or, 1 = ( x n ) ( x + 1 )
or, 1 = x 2 + x n x n
or, x 2 + ( 1 n ) x ( n + 1 ) = 0
but, stucked here. Is there any other way?
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Answers (2)

Esteban Johnson
Answered 2022-06-26 Author has 15 answers
To complete Ashvin Swaminathan's answer:
x = n 1 ± n 2 + 2 n + 5 2
Because x > 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

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landdenaw
Answered 2022-06-27 Author has 8 answers
Solve for x using the quadratic formula. As stated, there are infinitely many solutions...

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