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

Given:

Sum of squares of 2 consecutive even numbers is 452.

One number is x.

Answer:

Let the two consecutive even numbers be x and (x+2).

Now,

According to the question

=> x²+(x+2)²=452

{using (a+b)²= a²+b²+2ab}

we get,

=> x² +x²+4x+4=452

=> 2x²+ 4x+4-452=0

=> 2x²+4x-448=0

=> 2 ( x² +2x - 224) = 0

=> x² +2x - 224=0

By splitting the middle term

we get,

=> x² + 16x- 14x - 224=0

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

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

=> x= 14 and x = -16

As we cannot take negative value

so x=14 and the other number is 16. (14+2)

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Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Sum of squares = 452

1 number is equal to x

Assumption

Two consecutive even numbers = x and x + 2

So,

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

Splitting middle term

x² + 2x - 224 = 0

x² + 16x - 14x - 224 = 0

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

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

x = 14 and x = -16

Negative value is not acceptable

We get,

x = 14

So,

x + 2 = 14 + 2 = 16

Therefore,

Numbers are 14 and 16