Question

The sum of two integers is 7 then subracted to the square of second integer from the first and the result is 21

Answer 1

Answer:

The required two integers are 5 & 2.

Step-by-step-explanation:

Let the greater integer be x.

And the smaller integer be y.

From the first condition,

x + y = 7

⇒ x = 7 - y

⇒ x = - y + 7 - - - ( 1 )

From the second condition,

x² - y² = 21

⇒ ( - y + 7 )² - y² = 21

⇒ y² - 14y + 49 - y² = 21

⇒ - 14y + 49 = 21

⇒ 14y = 49 - 21

⇒ 14y = 28

⇒ y = 28 ÷ 14

⇒ y = 2

By substituting y = 2 in equation ( 1 ), we get,

x = - y + 7 - - - ( 1 )

⇒ x = - 2 + 7

⇒ x = 5

∴ The required two integers are 5 & 2.

Answer 2

STEP-BY-STEP EXPLANATION:

.

Let The integers are x and y respectively.

According To Question,

First Situation,

• Sum of Integers are 7.

So,

• ➺ x + y = 7 •••[1]

Second Situation,

• The difference of squares is 21.

So,

• ➺ x² - y² = 21

[a² - b² = (a + b)(a - b)]

• ➺ (x + y)(x - y) = 21
• ➺ 7(x - y) = 21
• ➺ x - y = 3 •••[2]

Adding Both Equations,

• ➺ (x + y) + (x - y) = 7 + 3
• ➺ x + y + x - y = 10
• ➺ 2x = 10
• ➺ x = 5

Substituting this value of x is Eq [1],

• ➺ x + y = 7 •••[1]
• ➺ y = 2

Hence,

• x = 5 and y = 2.

REQUIRED ANSWER,

• The Both Integers are 5 and 2 respectively.