Question

if the sum of two numbers is 437, then the find the absolute difference between the number with full soluction

Answer 1

1

x+y=42

xy=437

 

In 1st eqn solve for one variable in terms of the other;

x = 42-y

 

(42-y)y = 437

 

-y2+42y=437

y2-42y=-437

y2-42y+437=0

 

We can use quadratic equation   y = -b ±√(b2-4ac)

                                                           2a

 

y = 42 ±√((-42)2-4(1)(437))

                    2

 

y = 21 ±(√(1764 - 1748))/2

 

y = 21 ±(√16)/2

 

y = 21 ± 4/2

 

y = 21 ± 2

 

y = 21 or 23

 

If y = 21 then x+21=42 and x=21

Check:  xy=437  ...   21(21) = 441.... no

 

If y = 23  then x+23 = 42,  x=19

Check:  xy=437 ...  23(19) = 437 .... Yes

 

Our answer:  x= 19, y = 23

 Difference:  23-19 = 4