Question 38572
Let the numbers be x and y.
Then from the facts, we have
x - y = 11
sqrt(x) - sqrt(y) = 1
Let us solve the first one for x:
x = y + 11
Let us substitute that into the second equation.
sqrt(y + 11) - sqrt(y) = 1
We can rearrange this and then square both sides.
sqrt(y + 11) = sqrt(y) + 1
y + 11 = y + 2*sqrt(y) + 1
10 = 2*sqrt(y)
sqrt(y) = 5
y = 25
Thus x equals 36.