Question 169249
Solve the following system of nonlinear equations.
2xy=3
4x^2-8y^2=1
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From the 1st eqn, x = 3/2y
Sub for x into the 2nd eqn:
4(3/2y)^2 - 8y^2 = 1
9/(y^2) - 8y^2 = 1
Multiply by y^2
9 - 8y^4 = y^2
8y^4 + y^2 - 9 = 0
This is a quadratic in y^2
*[invoke solve_quadratic_equation 8,1,-9]
Factor:
(y^2 - 1)*(8y^2 + 9) = 0
y^2 = 1, -9/8
y = +1, -1
y = +i*(3/4)sqrt(2)
y = -i*(3/4)sqrt(2) (i = sqrt(-1) )