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

Answer:

a) x+2

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Answer 2

Answer:

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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