If the difference between squares of two consecutive even positive integers is 100, find the integers
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Let the two consecutive positive even numbers be x and (x+2)
According to the problem,
x
2
+(x+2)
2
=100
or, 2x
2
+4x+4=100
or, x
2
+2x−48=0
or, (x+8)(x−6)=0
∵x>0 this gives, x=6
So, the numbers are 6 & (6+2)=8.
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