Question

The product of two numbers is 48 and their sum is 19 . Find the numbers.

Answer 1

Step-by-step explanation:

Let the numbers be x and y,

x+y=19

x=19-y

And, xy=48

(19-y)y = 48

19y-y^2 =48

y^2 -19y+48 = 0

y^2-16y-3y+48=0

y(y-16) -3(y-16) =0

(y-16) (y-3) =0

y=16 , y=3

x=3 or x= 16

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Answer 2

Answer:

16 and 3

Step-by-step explanation:

Let the numbers be x and y.

x + y = 19  ------------------------(1)

xy = 48

Now,

(x - y)² = (x + y)² - 4xy

          = (19)² - 4(48) = 361 - 192

(x - y)² = 169

x - y = 13  ------------------------(2)

Adding (1) and (2),

(x + y) + (x - y) = 19 + 13

2x = 32

x = 16

By putting value of x in equation(1)

x + y = 19

16 + y = 19

y = 3

Therefore, the two numbers are 16 and 3.