# SOLUTION: Perfect Squares. Find a positive integer such that the integer increased by 1 is a perfect square and one-half of the integer increased by 1 is a perfect square. Also find the next

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: Perfect Squares. Find a positive integer such that the integer increased by 1 is a perfect square and one-half of the integer increased by 1 is a perfect square. Also find the next      Log On

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 Question 129389This question is from textbook : Perfect Squares. Find a positive integer such that the integer increased by 1 is a perfect square and one-half of the integer increased by 1 is a perfect square. Also find the next two larger positive integers that have this same property. (this is what I put x^2+1+1/2x^2+1)This question is from textbook Answer by 303795(595)   (Show Source): You can put this solution on YOUR website!First positive integer is 48. (48+1) = 49 (ie 7 squared) (48/2) = 24 (24+1) = 25 (ie 5 squared) . Next positive integer is 1680 (1680+1) = 1681 (ie 41 squared) (1680/2) = 840 (840+1) = 841 (ie 29 squared) . Next positive integer is 57120 (57120+1) = 57121 (ie 239 squared) (57120/2) = 28560 (28560+1) = 28561 (ie 169 squared) . Note if the condition that the integer had to be positive was not included then the first integer would be 0 (0+1) = 1 (ie 1 squared) (0/2) = 0 (0+1) = 1 (ie 1 squared) . Try also 1940448