SOLUTION: if john's grandmother age is a perfect square, and her age equals the square of his father's age less the square of his mother's age, 40, what is the age of his grandmother?
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Question 629012: if john's grandmother age is a perfect square, and her age equals the square of his father's age less the square of his mother's age, 40, what is the age of his grandmother?
g = f² - 40²
factor the right side:
g = (f - 40)(f + 40)
f has to be older that 40; otherwise, (f - 40)(f + 40) would not be positive.
If f were 42 or older, the grandmother would be 164 or older, which nobody
can be. So the father can only be 41
g = (41 - 40)(41 + 40)
g = (1)(81)
g = 81
And that is a perfect square. So the grandmother is 81.
Edwin
