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## Homework Statement

This is from Apostol's Calculus Vol. 1. Exercise 1.15, problem 6.(c)

Find all x>0 for which the integral of [t]

^{2}dt from 0 to x = 2(x-1)

## Homework Equations

[t] represents the greatest integer function of t.

## The Attempt at a Solution

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Integral of [t]

^{2}dt from 0 to x = {x(x-1)(2x-1)}/6, which on equating with 2(x-1) gives x(2x-1) = 12 which does not have a rational solution. The answers given at the back of the textbook are 1 and 5/2. Can someone please give me a hint as to where I'm going wrong?