x + y = 4
x^5 + y^5 = 464
find value of x and y
You asked:
Given \( x + y = 4 \), \( {x}^{5} + {y}^{5} = 464 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of equations has \(4\) solutions.
\[x = 2 - \sqrt{2}, y = \sqrt{2} + 2\]\[x = \sqrt{2} + 2, y = 2 - \sqrt{2}\]\[x = 2 - \sqrt{10} i, y = 2 + \sqrt{10} i\]\[x = 2 + \sqrt{10} i, y = 2 - \sqrt{10} i\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).