Find the solution of X, Y and Z of the following equations:
x + y^2 = 5
y = z^3+6
z = x^2-2 +y
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To find the solution for x, y, and z, we can substitute the given equations into each other to create a system of equations.
1) Substitute "y = z^3+6" into the equation "z = x^2-2 + y"
z = x^2 - 2 + (z^3 + 6)
Rearrange the equation:
x^2 - z^3 + z = 8
2) Substitute "y = z^3+6" into the equation "x + y^2 = 5"
x + (z^3 + 6)^2 = 5
x + z^6 + 12z^3 + 36 = 5
Rearrange the equation:
x + z^6 + 12z^3 + 31 = 0
Now we have a system of equations:
x^2 - z^3 + z = 8 (Equation 1)
x + z^6 + 12z^3 + 31 = 0 (Equation 2)
Unfortunately, this system cannot be easily solved algebraically. However, we can find numerical approximations for x, y, and z using numerical methods such as Newton's method or graphing the equations.
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