Question

2 numbers differ by 2 and their product is 360. Find the 2 numbers​

Answer 1

Step-by-step explanation:

Let the two numbers be x and y.

According to the question, x−y=2…(i)

Also, x×y=360

⇒x=

y

360

…(ii)

On putting the value of x=

y

360

in Eq. (i), we get

y

360

−y=2

⇒360−y

2

=2y

⇒y

2

+2y−360=0

⇒y

2

+20y−18y−360=0

⇒y(y+20)−18(y+20)=0

⇒(y−18)(y+20)=0

⇒y=−20 and 18

But y=−20 can't be the one number as it is given that the numbers are positive.

⇒y=18, then x=

18

360

=20

Hence, the two numbers are 20 and 18 .

Answer 2

The two numbers are 20 and 18.

Explanation :

Given :

• The difference between two numbers = 2.
• The product of two numbers = 360.

To Find :

• The two numbers.

Solution :

Let, the first number be x.

The second number be y.

According to the question,

⇒ x - y = 2 –––––(1)

⇒ xy = 360

⇒ x = $\sf \dfrac{360}{y}$ –––––(2)

Now, substitute the value of x in equation (1),

⇒ x - y = 2

⇒ $\sf \dfrac{360}{y}$ - y² = 2

⇒ 360 - y² = 2y

⇒ y² - 2y - 360 = 0

By splitting the middle terms,

⇒ y² + 20y - 18y - 360 = 0

⇒ y(y + 20) - 18(y + 20) = 0

⇒ (y - 18) (y + 20) = 0

⇒ (y - 18) = 0 ; (y + 20) = 0

⇒ y - 18 = 0 ; (y + 20) = 0

⇒ y = 18 ; y = -20

Hence, y = 18 because -20 is negative so it is not perfect for these.

Now, substitute the value of y in equation (2),

⇒ x = $\sf \dfrac{360}{y}$

⇒ x = $\sf \dfrac{360}{18}$

⇒ x = 20

Hence, the two numbers are 20 and 18.