Question

The sum of two numbers is 315. Find the numbers if their difference is 79.

Answer 1

Answer:

The numbers are 21 and 15.

Step-by-step explanation:

Let the two number = x and y

To find, the numbers = ?

According to question,

x + y = 36 ....(1)

And,

xy = 315 .....(2)

We know that,

(x-y)^2=(x+y)^2-4xy(x−y)

2

=(x+y)

2

−4xy

⇒ (x-y)^2=36^2-4(315)(x−y)

2

=36

2

−4(315)

⇒ (x-y)^2=1296-1260(x−y)

2

=1296−1260

⇒ (x-y)^2=6^2(x−y)

2

=6

2

x - y = 6 ....(3)

Adding (1) and (3), we get

x + x = 36 + 6 ⇒ 2x = 42

⇒ x = 21

Putting the value of x in (1), we get

21 + y = 36

⇒ y = 36 -21 = 15

Hence, the numbers are 21 and 15.

Step-by-step explanation:

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Answer 2

Answer:

let the two numbers be x and y respectively.

x+y=315------- 1

x-y=79---------- 2

Adding eqn. 1 and 2 simultaneously, we get,

2x=394

 x=394/2=197

Putting the value of x in eqn. 2,

Therefore, y=197-79=118

=>x=197  and y=118

Step-by-step explanation: