Solve the given equations: x2 + y2 = 34 x4 - y4 = 544 The values of x and y are

To solve this problem, use the algebraic identity for the difference of squares: x raised to the power of 4 minus y raised to the power of 4 can be written as the product of x squared plus y squared and x squared minus y squared.

Given that x squared plus y squared equals 34, substitute this into the equation 544 equals 34 times the quantity x squared minus y squared. Dividing 544 by 34 gives 16. Therefore, x squared minus y squared equals 16.

Now you have two simple equations:

1. x squared plus y squared equals 34
2. x squared minus y squared equals 16

Adding these two equations gives 2 times x squared equals 50, so x squared equals 25. This means x equals plus or minus 5.

Subtracting the second equation from the first gives 2 times y squared equals 18, so y squared equals 9. This means y equals plus or minus 3.

Thus, the values are x equals plus or minus 5 and y equals plus or minus 3, which corresponds to option B.