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$$\begin{eqnarray} x^3 + y^2 + x^2 y + xy & = & 91 \\ x^4 + 2x^2 y + y^2 &= & 169 \\ \end{eqnarray}$$

If positive integers x,y satisfy the system of equations above, what is the value of x+y?

Jun 24, 2020

#1
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The first one factors to

(x+y)(x^2+y) = 91

the second one factors to  (x^2+y)^2 = 169      sooooo    x^2 + y = 13   sub into the first equation above

(x+y)(13) = 91

x+y = 91/13 = 7

Jun 24, 2020