sum of two no. is 42 and multiplication of two no. 437. so what is the difference of two no.

Question

let the number's are x and y

X+Y=42

XY=437

 

so, find the difference of x and y

Answer 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                          

Answer 2

x+y=42

xy=437

 

we want to find x-y.we know that there is a relation between (x+y)² and (x-y)²  ,we can use that to find x-y easily

(x-y)²= (x+y)²-4xy

         = (42)² - 4*437    (put the values of x+y and xy)

         =1764 -1748

         = 16

 

So,  x-y = √(16) = 4

Answer 3

x + y = 42                eq1

xy = 437                  eq2

 

 

Our two numbers must be positive because the sum of two positives is a positive, and multiplying two positives gives us a positive. 

 

 

We have two equations with two unlike variables. We cannot solve them as they are, but we can substitute on equation into another.

 

Substitute eq1 into eq2.  We will get eq2 in terms of x.

 

x(42 - x) = 437

 

 

Distribute the x to get ride of parenthesis.

 

-x² + 42x = 437

 

 

Subtract 437 on both sides of the equation.

 

-x² + 42x - 437 = 0

 

 

We have a quadratic equation.   In these type of equations, we can solve for x using the famous quadratic formula:

 

x = (-b ± √(b² - 4ac)) / 2a

 

 

where:

a = -1

b = 42

c = -437

 

 

x = (-42 ± √(1764 - 4(437))) / -2

 

x = (-42 ± 4) / -2

 

x = (-42 - 4) / -2                   and               x =  (-42 + 4) / -2

 

x = 23                                   and               x = 19

 

 

We have two x values.  Therefore, we will have two y values.  Plug in these x values into eq1 to solve for y.

 

y = 42 - 23                and                  y = 42 - 19

 

y = 19                        and                 y = 23

 

 

The two numbers are 19 and 23.  They are both positive.

 

 

Difference = 23 - 19 = 4

 

Answer 4

As stated above, let the unknown numbers be X and Y.

 

Write down the basic equations.

x + y = 42

xy = 437

 

Now solve the first equation in terms of x or y. I have decided to solve it for y.

x + y = 42.

 

Subtract x from both sides.

x -x + y = 42 - x

 

Simplify.

y = 42 - x

 

Now, plug in 42 - x for y in the equation of xy = 437

xy = 437

 

Simplify.

x(42-x) = 437

 

Distribute.

42x -x² = 437

 

Rearrange so everything is on the same side.

-x² + 42x -437 = 0

 

Divide by -1 to get rid of the negative a term.

 

x² -42x + 437 = 0

 

Factor. Find 2 numbers that will multiply to get 437 and sum to get -42.

(x - 23)(x - 19) = 0

 

Set each equal to zero.

We get x = 23 and x = 19.

 

When you go back to look at the original problem, you realize that what you just solved works the same way. You just found 2 numbers which multiply to 437 and sum to 42. Therefor, x and y are 23 and 19 for this problem.

 

To find the difference, do 23 - 19 = 4.

 

The answer is 4.