Answer:
Step-by-step explanation:
You want the values of x and y that make (8-√x)(5+√x) ≡ 21 +y√x.
Solution
The product is ...
(8-√x)(5+√x) = 8·5 -5√x +8√x -(√x)²
Comparing this to the right-side expression, we see ...
40-x +3√x = 21 +y√x
Matching integer parts, we have ...
40 -x = 21
40 -21 = x = 19
Matching radical parts, we have ...
3√x = y√x
3 = y
The values of x and y are 19 and 3, respectively.
(8 -√19)(5 +√19) = 21 +3√19
