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How many perfect square possible (1/2/3) in following numbers. 1) a^2 + b + c 2) b^2 + a + c 3) c^2 + a + b

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How many perfect square possible (1/2/3) in following numbers.
1) a^2 + b + c
2) b^2 + a + c
3) c^2 + a + b

Given that a,b,c are positive integers.

posted Jul 25, 2017 by Salil Agrawal

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1 Answer

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No solution possible since
if a^2 = b+c and b^2 = a+c
then their difference a^2 - b^2 = b - a is true
but then since a^2 - b^2 = (a - b)(a + b)
(dividing both sides by (a + b) yields a + b = -1
which cannot occur if all three numbers are positive integers

answer Jul 26, 2017 by anonymous



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