Answer: the numbers are 16 and 31
Step-by-step explanation:
Let x represent one of the numbers.
Let y represent the other number.
The sum of the two numbers is 47. This means that
x + y = 47
The product of the numbers is 496. This means that
xy = 496 - - - - - - - - - - - -1
Substituting x = 47 - y into equation 1, it becomes
y(47 - y) = 496
47y - y² = 496
y² - 47y + 496 = 0
y² - 16y - 31y + 496 = 0
y(y - 16) - 31(y - 16) = 0
(y - 31)(y - 16) = 0
y = 31 or y = 16
x = 47 - 16 = 31
The numbers are 16 and 31.
Given that the sum of the two numbers is 47.
If one number is x then the other number is (47 - x).
Given: Product = 496.
So,
[tex]x(47 - x) = 496\\ 47x-x^2=496\\ x^2-47x+496=0\\ (x-16)(x-31)=0\\ x=16, 31[/tex]
For x = 16, other number is 47 - 16 = 31.
For x = 31, other number is 47 - 31 = 16.
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