National and Regional Contests USA Contests USA - Other Middle and High School Contests Math Prize For Girls Problems 2010 Math Prize For Girls Problems 1 Math Prize 2010 Problem 1 Problem Statement If a a a b b b ∣ a ∣ ≠ ∣ b ∣ \left| a \right| \ne \left| b \right| ∣ a ∣ = ∣ b ∣ ( b 2 a 2 + a 2 b 2 − 2 ) × ( a + b b − a + b − a a + b ) × ( 1 a 2 + 1 b 2 1 b 2 − 1 a 2 − 1 b 2 − 1 a 2 1 a 2 + 1 b 2 ) .
\left( \frac{b^2}{a^2} + \frac{a^2}{b^2} - 2 \right) \times
\left( \frac{a + b}{b - a} + \frac{b - a}{a + b} \right) \times
\left(
\frac{\frac{1}{a^2} + \frac{1}{b^2}}{\frac{1}{b^2} - \frac{1}{a^2}}
- \frac{\frac{1}{b^2} - \frac{1}{a^2}}{\frac{1}{a^2} + \frac{1}{b^2}}
\right).
( a 2 b 2 + b 2 a 2 − 2 ) × ( b − a a + b + a + b b − a ) × ( b 2 1 − a 2 1 a 2 1 + b 2 1 − a 2 1 + b 2 1 b 2 1 − a 2 1 ) .