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The sum of the squares of two consecutive positive even integers is 52.Find the integers

2 Answers

2 votes

Answer:

4 and 6


Explanation:

one number = x

other number = x + 2


x² + (x + 2)² = 52

x² + x² + 4x + 4 = 52

2x² + 4x - 48 = 0

x² + 2x - 24 = 0

(x - 4)(x + 6) = 0

x = 4 or x = -6


Since x is positive

x = 4

x + 2 = 6

User S Rivero
by
8.3k points
1 vote

Answer:

The two consecutive positive integers are
4 and
6.

Explanation:

Let
x be an even integer, then the next even integer is
(x+2).


The sum of the squares of these even integers is
52.


We can write the following equation and solve for
x.



x^2+(x+2)^2=52.

We expand to get,


x^2+x^2+4x+4=52.

We simplify to get,


2x^2+4x+4-52=0.


This gives us,


2x^2+4x-48=0


We divide through by 2 to get,


x^2+2x-24=0.

This is now a quadratic trinomial

We split the middle term to get,



x^2+6x-4x-24=0.


We factor to obtain,


x(x+6)-4(x+6)=0



\Rightarrow (x+6)(x-4)=0



\Rightarrow (x+6)=0 or (x-4)=0



\Rightarrow x=-6 or x=4


We discard
x=-6 since it is not a positive integer.


\therefore x=4


Hence the two consecutive positive even integers are,


4

and


4+2=6








User Myk
by
8.7k points

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