An algebra problem by Theodore Jonathan

Algebra Level pending

How many positive real integers for (x,y) that satisfy

4 × x + y + 4 × ( x y ) 1 2 − 36 × x 1 2 − 18 × y 1 2 + 80 = 0 4 \times x + y + 4 \times (xy)^\frac{1}{2} - 36 \times {x}^\frac{1}{2} - 18 \times {y}^\frac{1}{2} + 80 = 0 ?


The answer is 11.

Theodore Jonathan by Theodore Jonathan , 19, Singapore

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