Official Guide Explanation:
Problem Solving #227

Background

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Solution and Metadata

Question: 227
Page: 185
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Solving Quadratic Equations > Difference of Squares
Category 2: Algebra > Solving Quadratic Equations > Squares
Category 3: Algebra > Linear Equations-Two Unk >

Explanation: 2xy may look familiar to you as a common middle term in a squared binomial, as in (x - y)² = x²-2xy + y². To come up with 2xy from the equations given, square each one, resulting in the following:

x² + 2xy + y² = a²

x²-2xy + y² = b²

To isolate 2xy, subtract the second equation from the first one, resulting in:

4xy = a²-b²

2xy = ((a²-b²)/2), choice (A).

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