SOLUTION: 27x^3+y^3=35; xy=2; find 3x+y

Question 998683: 27x^3+y^3=35; xy=2; find 3x+y
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
= ;
= .

Find 3x+y.
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Express y from the second equation y = and substitute into the first one. You will get

= ,

Multiply both sides by . You will get

= ,     or

= .

Introduce new variable z = . You will get a quadratic equation

= .

Now, apply the quadratic formula to solve it. You will get

z = = .

So, = 1     -----> x = 1, y = 2.

=     -----> x = , y = .

Answer. Two solutions: 1) x = 1, y = 2;   and 2) x = , y = .

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