Given, 2^2x-y = 32

=> 2^2x-y = 2⁵

When base are equal, then we can equate exponent, So we get

=> 2x - y = 5 ..............1

Again given, 

2^x+y = 16

=> 2^x+y = 2⁴

When base are equal, then we can equate exponent, So we get

=> x + y = 4 ..............2

Now, add equation 1 and 2, we get

      2x - y + x + y = 5 + 4

=> 3x = 9

=> x = 9/3

=> x = 3

From equation 2, we get

     3 + y = 4

=> y = 4 - 3

=> y = 1

So, x² + y² = 3² + 1²

              = 9 + 1

              = 10 

Hence, x² + y² = 10