If x⁴ ≤ 16 and y² ≤ 36, then the maximum possible value of (x - y) is:

Question: If x⁴ ≤ 16 and y² ≤ 36, then the maximum possible value of (x - y) is:

Solution:
Given that,
x⁴ ≤ 16
⇒ x⁴ ≤ 2⁴
⇒ x ≤ 2
∴ -2 ≤ x ≤ 2
And
y² ≤ 36
⇒ y² ≤ 6²
⇒ y ≤ 6
∴ - 6 ≤ y ≤ 6

Now,
x could be positive 2 or negative 2. y could be positive 6 or negative 6 . The four possible values for (x - y) are as follows,
1. 2 - 6 = - 4 ; [When x = 2 and y = 6]
2. 2 - (- 6) = 2 + 6 = 8 ; [When x = 2 and y = - 6]
3. - 2 - 6 = - 8 ; [When x = - 2 and y = 6]
4. - 2 - (- 6) ​= - 2 + 6 = 4 ; [When x = - 2 and y = - 6]

So the maximum value would be 8.