Question

Sum of the squares of two consecutive even numbers is 452.

a) If one number is 'x' , then what is the next number ?

b) Form the second degree equation and find the numbers​

Answer 1

Answerif x has to be positive, then the numbers are 14 and 16

Step-by-step explanation:

Given - the first number is x.

Thus, the next number is x + 2 ---- (a)

And,

x² + (x+2)² = 452 ---- (b)

or, x² + x² + 4x + 4 = 452

or, 2x²  + 4x - 448 = 0

x² + 2x - 224 = 0

or, x² - 14x + 16x -224 = 0

or, x (x - 14) + 16(x - 14) = 0

hence, (x+16)(x-14) = 0

therefore, x = -16 or 14

but, x has to be positive, so x = 14

Answer 2

Answer:

• Required numbers are 14 and 16.

Step-by-step explanation:

Given:

• Sum of squares of two consecutive even numbers = 452.
• One number = 'x'.

To Find:

• The numbers.

According to question,

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.