The difference of a positive integer and its inverse is 15/4. Find the integer.

Question

SAT

Adrian Conrad

15 September, 03:32

The difference of a positive integer and its inverse is 15/4. Find the integer.

+5

Answers (1)

Know the Answer?

Wayne Cooke · Answer 1

X - 1/X = 15/4

X/1 - 1/x = 15/4

X • (X/1) - 1/X = 15/4

X ^2 - 1/X = 15/4

X • (X ^2 - 1/X) = 15/4 • X

X^2 - 1 = 15x/4

4 • (X ^2 - 1) = 15x/4 • 4

4 (X^2 - 1) = 15x

4x ^2 - 4 = 15x

4x^2 - 15x - 4 = 0

4x^2 - 15x = 4

X (4x - 15) = 4.

X = 4

4x - 15 = 4

4x = 19

4x/4 = 19/4

X = 19/4.

I believe the solution is 4.

4/1 - 1/4 = 15/4

16/4 - 1/4 = 15/4

15/4 = 15/4.