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2020 AMC 10A Problems/Problem 14

Revision as of 21:02, 31 January 2020 by Luckylw (talk | contribs) (Created page with "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}...")
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Real numbers $x$ and $y$ satisfy $x + y = 4$ and $x \cdot y = -2$. What is the value of\[x + \frac{x^3}{y^2} + \frac{y^3}{x^2} + y?\] $\textbf{(A)}\ 360\qquad\textbf{(B)}\ 400\qquad\textbf{(C)}\ 420\qquad\textbf{(D)}\ 440\qquad\textbf{(E)}\ 480$

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