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Finding minimum value of expression and solving an equation.

Source: Vietnam MO 1984 P4

March 20, 2011

calculusintegrationquadraticsnumber theoryalgebra unsolvedalgebra

Problem Statement

(a)

Let

x, y

be integers, not both zero. Find the minimum possible value of

|5x^2 + 11xy - 5y^2|

(b)

Find all positive real numbers

t

such that

\frac{9t}{10}=\frac{[t]}{t - [t]}