Question

The sum of the squares of
consecutive positive even intergers is 340. Find the integers.
​

Answer 1

Question:

The sum of the squares of  consecutive positive even integers is 340. Find the integers.

Given:

• The sum of squares consecutive positive even numbers = 340

• Let one number be y and the other (y + 2)

To Find:

The Integers whose sum of squares is 340

Solution:

$(y)^2+(y+2)^2=340\\\\\\y^2+y^2+4y+4=340\\\\\\2y^2+4y=340-4\\\\\\2y^2+4y=336\\\\\\2y^2+4y-336=0\\\\\\(2y+28x)(y-12)=0\\\\\\y=-14\:\:or\:\: 12$

y = 12 Since they asked the integers to be positive

• y = 12

• y + 2 = 12+2 = 14  

Verification:

$(12)^2+(14)^2=340\\\\\\144 + 196 = 340\\\\\\340 =340\\\\\\\textsc{L.H.S = R.H.S}$

Answer:

Therefore the numbers are 12 , 14

Be Brainly!