Then I’d Rather Not Know

Mrs Holmann could not take it any longer that everyone kept asking her about her son’s age. This time she made her answer complicated enough for people never to ask again… neither her son’s age, nor her own! She said: “If you square my age and subtract the square of my son’s, the number you get is exactly 2 times the square of the difference between our ages. Also, if you square his age and you add it to the square of mine, the number you get is exactly 7776 less than 4 times the square of the sum of our ages!”

Can you work out how old they are?

[Note: this problem was written by Zsuzsanna Sukosd, a 15-year-old high school math student from Denmark.]

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