Answer:
There are no two numbers whose product is 52 and whose sum is 11.
Explanation:
give the 1st number is x and the 2nd number is y, then
x + y = 11 and xy = 52
x + y = 11 => y = 11 - x
x(11 - x) = 52
11x - x^2 = 52
=> x^2 - 11x + 52 = 0
Using quadratic formula: ax^2 + bx + c = 0
with a = 1, b = -11, c = 52
=> x = [-b ± √(b^2 - 4ac)]/2a
=> x = [-(-11) ± √((-11)^2 - 4x1x52)]/2x1
=> x = [11 ± √(121 - 208)]/2
=> x = [11 ± √(-87)]/2
Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, there are no two numbers whose product is 52 and whose sum is 11.