Difference between revisions of "1987 AHSME Problems/Problem 15"
(Created page with "==Problem== If <math>(x, y)</math> is a solution to the system <math>xy=6 \qquad \text{and} \qquad x^2y+xy^2+x+y=63</math>, find <math>x^2+y^2</math>. <math>\textbf{(A)}\ 13 \q...") |
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\textbf{(E)}\ 81 </math> | \textbf{(E)}\ 81 </math> | ||
+ | ==Solution== | ||
+ | First note that <math>x^2y+xy^2+x+y= (xy+1)(x+y)</math>. Substituting <math>6</math> for <math>xy</math> gives <math>7(x+y)= 63</math>, giving a result of <math>x+y=9</math>. Squaring this equation and subtracting by <math>12</math>, gives us <math>x^2+y^2= \boxed{69}</math> | ||
== See also == | == See also == |
Revision as of 23:05, 26 August 2016
Problem
If is a solution to the system , 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 | |
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All AHSME Problems and Solutions |
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