Question

The sum of the square of two consecutive natural numbers is 452. Find the numbers.

Answer 1

Given:

• Sum of squares of two consecutive even

numbers =452 .

One number =^ prime x^ prime .

To Find:

The numbers.

According to question,

Let two consecutive even numbers be 'x' and 'x

+ 2!

=>x^ 2 +(x+2)^ 2 =452

=>x^ 2 +x^ 2 +4+4x=452

=>2x^ 2 +4x=452-4

=>2x^ 2 +4x=448

=>2x^ 2 +4x-448=0

=>x^ 2 +2x-224=0

Now, we will solve this equation by splitting middle term method,

=>x^ 2 +2x-224=0

=>x^ 2 +16x-14x-224=0

=>x(x+16)-14(x+16)=0

=>(x-14)(x+16)=0

=> x=14 and -16

Hence, required numbers are 14 and 16.

Answer 2

Let two consecutive even numbers be 'x' and 'x + 2'.

=> x² + (x + 2)² = 452

=> x² + x² + 4 + 4x = 452

=> 2x² + 4x = 452 - 4

=> 2x² + 4x = 448

=> 2x² + 4x - 448 = 0

=> x² + 2x - 224 = 0

Now, we will solve this equation by splitting middle term method,

=> x² + 2x - 224 = 0

=> x² + 16x - 14x - 224 = 0

=> x(x + 16) - 14(x + 16) = 0

=> (x - 14)(x + 16) = 0

=> x = 14 and - 16

Hence, x = 14

And, x + 2 = 16.

Hence, required numbers are 14 and 16.