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Let x and y be real numbers satisfying two conditions: x-y=5 and xy=7. Find x^3y+xy^3​

User Tom Dunham
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1 Answer

6 votes

We can factor


x^3y+xy^3 = xy(x^2+y^2) = xy[(x-y)^2+2xy]

And now we know all the terms involved: substitute every occurrence of xy with 7 and every occurrence of x-y with 5 to have


xy[(x-y)^2+2xy]=7\cdot(5^2+2\cdot 7) = 7\cdot (25-7) = 7\cdot 18 = 126

User Johan Carlsson
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