Question

The product of 2 consecutive even integers is 528 find the value of each integers

Answer 1

Answer :-

• Value of two integers are 22 and 24

Explanation:

Given :-

• The product of 2 consecutive even integers is 528

To Find :-

• Value of each integers

Solution :-

• Let one integer be x
• other integer be x + 2

According to question,

• Product of two integers = 528

↠ (x)(x + 2) = 528

↠ x² + 2x = 528

↠ x² + 2x - 528 = 0

↠ x² + 24x - 22x - 528 = 0

↠ x(x + 24) - 22 (x + 24) = 0

↠ (x + 24) (x - 22) = 0

↠ x = -24 or 22

Hence,

• 1st integer = 22
• 2nd Integer = 22 + 2 = 24

Value of two integers are 22 and 24

Answer 2

Explanation:

It is given that, The product of 2 consecutive even integers is 528 and we have to find the value of each integers.

• So, Let us assume the 1st consecutive even integer as y and the 2nd as (y + 2)

Now, As it is stated in the question that the product of 2 consecutive even integers is 528, So

`\\ { \longrightarrow \qquad{ \pmb{ \sf { y(y + 2) = 528 }}}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \pmb{ \sf { {y}^(2) + 2y = 528 }}}} \: \: \\ \\`

Subtracting both sides by 528 we get :

`\\ { \longrightarrow \qquad{ \pmb{ \sf { {y}^(2) + 2y - 528= 528 - 528 }}}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \pmb{ \sf { {y}^(2) + 2y - 528= 0 }}}} \: \: \\ \\`

We have to find two numbers such that,

`\\ { \longrightarrow \qquad{ \pmb{ \sf { p + q= 24 }}}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \pmb{ \sf { p * q= 528 }}}} \: \: \\ \\`

The two numbers are 24 and 22. So,

`\\ { \longrightarrow \qquad{ \pmb{ \sf { {y}^(2) + (-22y) + 24y - 528= 0 }}}} \\ \\`

`{ \longrightarrow \qquad{ \pmb{ \sf { {y}(y -22) + 24(y - 22)= 0 }}}} \\ \\`

`{ \longrightarrow \qquad{ \pmb{ \sf { (y -22) (y + 24)= 0 }}}} \\ \\`

• Whether, the value of y is (-24) or 22.

`\:`

So, The first consecutive even integer is 22.

Now,

`\\ { \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=y \:+2 \: }}}} \\ \\`

`{ \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=2 2+2 \: }}}} \\ \\`

`{ \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=24 }}}} \\ \\`

Therefore,

• The value of each integer is 22 and 24.