Answer: Hence Pair( x, y) = [ 105/2, 105/2]
Step-by-step explanation:
Given that;
Among all pairs of numbers with a sum of 105;
the pair whose product is maximum = ?
so let pairs of numbers with a sum of 105 be x and y respectively
x + y = 105
let y = 105 - x
now
product = xy = x( 105 - x ) = 105x - x²
now
p(x) = 105x - x²
for maximum value of p
dp/dx =0
⇒ dp/dx = 105 - 2x = 0
2x = 105
x = 105/2
y + x = 105
y = 105 - x
y = 105 - 105/2 = 105/2
Hence Pair( x, y) = [ 105/2, 105/2]
Answer is on the picture and all the work that I showed

Here, we want to get what Andre's mistake was and correct it
To answer this, we are supposed to use the division law of indices
We have this as;

Now, in the case of this question, x is 4 and y is -3
So, we have the expression as;

His mistake is thus adding the exponents instead of subtracting
What do we need to find in your question?