Question

the difference between 2 numbers is 20 and there product is 125 what are the numbers

Answer 1

Answer:

Hey buddy here is your answer........

Step-by-step explanation:

We have 2 unknown numbers, then we can define them as:

x: Unknown number 1

y: Unknown number 2

The problem states that "the difference of two numbers is 20". We can translate this to x - y = 20

We also know that "their product is 125". We can translate this to x . y = 125

Putting both equations together, we get the following system of equations

Now, to solve this system of equations we can use the Substitution Method.

We can solve 1st equation for x, by adding y to both sides

x - y + y = 20 + y

x = 20 + y

We can substitute x by 20 + y on the 2nd equation

(20 + y) . y = 125

Applying distributive property on the left side

20y + y² = 125

Substracting 125 to both sides and rearranging the terms, we get

20y + y² - 125 = 125 -125

y² + 20y - 125 = 0

We can apply the quadratic equation attached to solve this (with a = 1, b = 20, c = -125).

( -20 ± √(20² - 4 . 1 . -125) ) / ( 2. 1 ) =

( -20 ± √(400 + 500) ) / ( 2) =

( -20 ± √900 ) / ( 2) =

( -20 ± 30 ) / ( 2) =

We get 2 results:

y1 = (-20 + 30) / 2 = 5

y2 = (-20 - 30) / 2 = -25

For each of these values of y, we can find the corresponding value of x:

x1 = 20 + y1 = 20 + 5 = 25

x2 = 20 + y2 = 20 + (-25) = -5

Hope you understand this...............and please mark me as brainlist.........

Answer 2

Answer:

5 and 25 or -5 and -25

Step-by-step explanation:

let a and b be the required numbers,

given: a-b= 20 => a= 20+b, and a×b=125

therefore, (20+b)b= 125

b^2 + 20b - 125= 0

or, b^2 +25b -5b -125 = 0

or, b(b+25) -5(b+25)=0

or, (b+25)(b-5)=0

either (b+25)=0 or, (b-5)=0

b= -25. or, b=5

therefore, a= -5 or 25