Question

The difference of two numbers is 2 and their product is 80

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Let the larger number = x and smaller number = y

We have to find, the values of two numbers are:

Solution:

According to question,

The difference of two numbers = 2

∴ x - y = 2              .......... (1)

Also, xy = 80        .......... (2)

∴ $(x+y)^{2} =(x-y)^2+4xy$

Using equations (1) and (2), we get

$(x+y)^{2} =2^2+4(80)$

⇒ $(x+y)^{2}$ = 4 + 320 = 324

⇒ $(x+y)^{2}$ = $18^2$

x + y = 18             .......... (3)

Adding equations (1) and (3), we get

x - y + x + y = 2 + 18    

⇒ 2x = 20

⇒ x = 10

Put x = 10 in equation (1), we get

10 - y = 2  

⇒ y = 8

∴ x = 10 and y = 8

Thus, the two numbers are "10 and 8".