Question

The sum of the squares of two consecutive positive even odd numbers is 52. Find the number.​

Answer 1

Answer:

Let the consecutive positive even numbers be x and x + 2

. From the given information, x2 + (x + 2)2 = 52

2x2 + 4x + 4 = 52

2x2 + 4x − 48 = 0 x2 + 2x − 24 = 0

(x + 6) (x − 4) = 0 x = − 6, 4 Since, the numbers are positive, so x = 4 Thus, the numbers are 4 and 6

Answer 2

Information provided with us:

• The sum of the squares of two consecutive positive even odd numbers is 52.

What we have to calculate:

• We have to calculate and find out the number.

Performing Calculations:

_________________

Let us assume that,

• First number be y
• Thus, second number would be (y + 2)

Doing the squares,

⇒(y)² + (y + 2)² = 52

Opening brackets,

⇒ y² + y (y + 2) + 2 (y + 2) = 52

⇒ y² + y² + 2y + 2y + 4 = 52

⇒ 2y² + 2y + 2y + 4 = 52

⇒ 2y² + 4y + 4 = 52

Transposing 52 to R.H.S.,

⇒ 2y² + 4y + 4 - 52 = 0

On subtracting 52 by 4 we gets,

⇒ 2y² + 4y - 48 = 0

Dividing by 2,

⇒ y² + 2y - 24 = 0

Forming factors,

⇒ y² + 6y - 4y - 24 = 0

Grouping them,

⇒ y (y + 6) - 4 (y + 6) = 0

⇒ (y + 6) (y - 4) = 0

Comparing,

⇒ y = 4

Hence, first number is 4.

Finding out second number,

⇒ Second number = y + 2

⇒ Second number = 4 + 2

⇒ Second number = 6

Hence, the numbers are 4 and 6.