Difference between revisions of "2020 AMC 10A Problems/Problem 14"
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Real numbers <math>x</math> and <math>y</math> satisfy <math>x + y = 4</math> and <math>x \cdot y = -2</math>. What is the value of<cmath>x + \frac{x^3}{y^2} + \frac{y^3}{x^2} + y?</cmath> | Real numbers <math>x</math> and <math>y</math> satisfy <math>x + y = 4</math> and <math>x \cdot y = -2</math>. What is the value of<cmath>x + \frac{x^3}{y^2} + \frac{y^3}{x^2} + y?</cmath> | ||
<math>\textbf{(A)}\ 360\qquad\textbf{(B)}\ 400\qquad\textbf{(C)}\ 420\qquad\textbf{(D)}\ 440\qquad\textbf{(E)}\ 480</math> | <math>\textbf{(A)}\ 360\qquad\textbf{(B)}\ 400\qquad\textbf{(C)}\ 420\qquad\textbf{(D)}\ 440\qquad\textbf{(E)}\ 480</math> | ||
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| + | ==See Also== | ||
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| + | {{AMC10 box|year=2020|ab=A|num-b=13|num-a=15}} | ||
| + | {{MAA Notice}} | ||
Revision as of 21:03, 31 January 2020
Real numbers 
and 
satisfy 
and 
. What is the value of![\[x + \frac{x^3}{y^2} + \frac{y^3}{x^2} + y?\]](http://latex.artofproblemsolving.com/1/b/7/1b77f92edbab9a6134e14217ee0c56700cef3dbf.png)
See Also
| 2020 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
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