Difference between revisions of "1987 AHSME Problems/Problem 15"
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If <math>(x, y)</math> is a solution to the system | If <math>(x, y)</math> is a solution to the system | ||
− | <math>xy=6 | + | <math>xy=6</math> and <math>x^2y+xy^2+x+y=63</math>, |
find <math>x^2+y^2</math>. | find <math>x^2+y^2</math>. | ||
Latest revision as of 11:36, 31 March 2018
Problem
If is a solution to the system and , find .
Solution
First note that . Substituting for gives , giving a result of . Squaring this equation and subtracting by , gives us
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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