SOLUTION: If n is the first of two consecutive even integers, write an equation that can be used to find the integers if the sum of the squares of twice the first and the second is 100.
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Question 733158: If n is the first of two consecutive even integers, write an equation that can be used to find the integers if the sum of the squares of twice the first and the second is 100.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If n is the first of two consecutive even integers,
write an equation that can be used to find the integers
if the sum of the squares of twice the first and the second is 100.
:
let n and (n+2) = the two even consecutive integers
:
the sum of the squares of twice the first and the second is 1
(2x)^2 + (x+2)^2 = 100
4x^2 + x^2 + 4x + 4 = 100
5x^2 + 4x + 4 - 100 = 0
5x^2 + 4x - 96 = 0
Factors to
(5x+24)(x-4) = 0
the integer solution
x = 4
:
The two consecutive even integers: 4, 6
:
:
Check 8^2 + 6^2 = 100
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