SOLUTION: Hello! Can somebody help please? My question is: Last time it was the kids birthdays I noticed that even though they were born only one year apart, when I squared their ages

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Question 41901: Hello!
Can somebody help please?
My question is:
Last time it was the kids birthdays I noticed that even though they were born only one year apart, when I squared their ages and then added the sum of the ages they would total 1105. How old are my kids?
Thanks. Your help and time are much appreciated.
marangeo
Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website!
Okay let their ages be x and x+1, since they are a year apart. Then we have
x^2 + (x+1)^2 + x + x+1 = 1105
Now solve this...
x^2 + x^2 + 2x + 1 + x + x + 1 = 1105
2x^2 + 4x + 2 = 1105
2x^2 + 4x - 1103 = 0
This is not factorable, so we use the quadratic formula to get
x = (-4 � sqrt(16 + 8824)) / 4
x = (-4 � sqrt(8840)) / 4
x = (-4 � 2*sqrt(2210)) / 4
x = (-2 � sqrt(2210)) / 2
x is about 22.5 years old
x+1 is about 23.5 years old
I have a feeling there is something wrong with the problem...