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## Homework Statement:

- Find all x>0 for which $$\int_0^x [t]^{2} dt = 2(x-1) $$

## Relevant Equations:

- The notation [x] denotes the greatest integer less than or equal to x

In the question above it, the author (Apostol) states: $$\int_0^n [t]^{2} dt = \frac{n(n-1)(2n-1)}{6}$$

Why can't I set the two equations = and get the result?

2(x-1) = x(x-1)(2x-1)/6 => 12 = 2x^2 - x => 0 = x^2-(x/2) -6

using quadratic equation I get the wrong answer

Why can't I set the two equations = and get the result?

2(x-1) = x(x-1)(2x-1)/6 => 12 = 2x^2 - x => 0 = x^2-(x/2) -6

using quadratic equation I get the wrong answer