The sum of 2 numbers is 92. The product of those two numbers is 2052. What are these two numbers?

Question

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Answer 1

x + y = 92
xy = 2052
y = 2052 / x

x + 2052 / x = 92
x² + 2052 = 92 x
x² - 92x + 2052 = 0
x = [ 92 ± √(92² - 8208) ] / 2
x = [ 92 ± √(256) ] / 2
x = [ 92 ± 16 ] / 2
x = 54, x = 38

Answer 2

Let x = 1st number
Then 92 - x = 2nd number
Since the product is given, x(92- x) = 2052
92x - x^2 = 2052
92x - x^2 - 2052 = 0
since I like positive x^2 values, multiply each term by -1
x^2 - 92x + 2052 = 0
(x - 38)(x - 54) = 0
x = 38; 54

Answer 3

A + B = 92
AB = 2052

A ( 92 - A ) = 2052
92A - A² = 2052

A² - 92A + 2052 = 0

( A - 54 ) ( A - 38 ) = 0

The two numbers are 54 and 38.

Answer 4

Solve the simultaneous equations:
x + y = 92
x * y = 2052
x * (92 - x) = 2052
92x - x^2 = 2052
x^2 - 92x + 2052 = 0
(x-38)*(x-54) = 0
x = 38, 54

So the numbers are 38 and 54.

Answer 5

The numbers are 38 and 54.

Answer 6

x+y=92 and x*y=2052
x=92-y and (92-y)y=2052

-y^2+92y-2052=0

y= 38
x=54

Answer 7

54 and 38.

Answer 8

this type of problem gets asked here frequently, although the problem may change. so i'll give the general solution:

a+b=x (in this case, x is 92)
ab=y (in this case, y is 2053)

solve first equation for a:
a = x-b
substitute into second equation
(x-b)b=y
b^2 -bx + y = 0
use quadratic equation to solve for b
(or factor if can be easily done)

plug b into earlier equation to find a:
a = x-b

Answer 9

38,54