What is the value of aboslute value:| xy |
1: x² + y² = 10
2: x²-y² = 6
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Find absolute value:| xy |
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S1:: We could have x = 3, y = 1, or x = √10, y = 0. Not sufficient.
S2:: Same idea! We could have x = √7, y = 1, or x = √6, y = 0. Not sufficient.
S1 + S2::
Add the two together, yielding 2x² = 16, or x² = 8, or |x| = 2√2.
Now subtract the first from the second, yielding 2y² = 4, or y² = 2, or |y| = √2.
|xy| = |x| * |y|, so |xy| = 2√2 * √2, or 4.
(Footnote: the solution plot is quite lovely.
)
S2:: Same idea! We could have x = √7, y = 1, or x = √6, y = 0. Not sufficient.
S1 + S2::
Add the two together, yielding 2x² = 16, or x² = 8, or |x| = 2√2.
Now subtract the first from the second, yielding 2y² = 4, or y² = 2, or |y| = √2.
|xy| = |x| * |y|, so |xy| = 2√2 * √2, or 4.
(Footnote: the solution plot is quite lovely.
)
