We are required to find the value of two numbers that has a difference of 24 and a product of 585
The value of the two numbers are 39 and 15 respectively
let
the two numbers = x and y respectively
x - y = 24 (1)
xy = 585 (2)
from (1)
x = 24 + y
Recall,
xy = 585
(24 + y) × y = 585
24y + y² = 585
y² + 24y - 585 = 0
solve quadratic equation using factorization method
The factors are 39 and -15
y² + 39y - 15y - 585 = 0
y(y + 39) -15(y + 39) = 0
(y - 15) (y + 39) = 0
y - 15 = 0 or y + 39 = 0
y = 15 or y = - 39
The value of y can not be negative
So,
y = 15
substitute into (1)
x - y = 24
x - 15 = 24
x = 24 + 15
x = 39
Therefore,
the value of x and y is 39 and 15 respectively.
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