SOLUTION: Solve for x and y if 4xy=-15 and 4x^3+4y^3=49

Question 1094574: Solve for x and y if 4xy=-15 and 4x^3+4y^3=49
Answer by ikleyn(52832) (Show Source): You can put this solution on YOUR website!
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Solve for x and y if 4xy=-15 and 4x^3+4y^3=49
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4xy = -15                    (1)
4x^3 + 4y^3 = 49             (2)


HINT.  Use this trick:  Raise both sides of the eq(1) to degree 3.  You will get


64x^3*y^3 = -3375,           (3)
4x^3 + 4y^3 = 49.            (4)


Introduce new variables  u = x^3, v = y^3.  Then the system (3),(4) takes the form

64uv = -3375,
4u + 4v = 49.


In this way you reduced your quite complicated system to much more simple.


The rest is just a standard exercise in solving quadratic equation.

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