Question

The product of two consecutive even natural no is 224 find the no

Answer 1

AnswEr:

• Consecutive numbers are the numbers that follow each other in order. They have a difference of 1 in each Number.

Let the two Consecutive even natural Numbers are 2x & 2x+2.

According to Question

Product of these numbers:

2x (2x + 2) = 224

4x² + 4x = 224

Dividing both sides by 4

x² + x - 56 = 0

( x - 7) (x + 8) = 0

=> x = 7 & x = -8

We can't take negative Value.

Therefore

Answer is 7

Answer 2

$\huge\bf{Answer :}$

Given :-

• The two numbers are even numbers and also consecutive.
• Their product is 224.

To find :-

• The two numbers.

Explanation :-

We know that the consecutive numbers are those continuous numbers that follows each other without any gap or intervals.

Here, 1,2,3,4,5,6, and so on is considered as consecutive numbers because they comes after one another without any gap.

Now, let's solve the question!

Let the first number be 2x.

∴ Another Number = 2x + 2

[ Here these numbers are chosen because it is given that they are consecutive even natural number. ]

A•T•Q

Product of the numbers = 224

⇒ (2x)(2x+2) = 224

• Opening brackets.

☆ 4x² + 4x = 224

• Dividing both sides by 4. ( To make calculations easier. )

⇒ x² + x = 56

⇒ x² + x - 56 = 0

• Solving the quadratic equation by prime factorisation using splitting the middle term.

⇒ x² + 8x - 7x - 56 = 0

⇒ x ( x + 8 ) - 7 ( x + 8 ) = 0

⇒ ( x - 7 ) ( x + 8 ) = 0

∴ ( x -7 ) = 0 or ( x + 8 ) = 0

Hence, x = 7 or x = -8

( It is given that the numbers are natural numbers and cannot be negative. )

Therefore, we'll take the value of x = 7

Now, First number = 2x = 2 × 7 = 14 ✔️

And, Another number = 2x + 2 = 2 × 4 + 2 = 16 ✔️

Therefore, the required numbers are 14 and 16.

$\huge\bf{Extra\: Information :}$

1) We can find the other consecutive numbers if a specific number is given, by the formula :-

n, (n+1), (n+2), (n+3), (n+4), and so on.

Where, n = specific number.