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If 200 is added to a positive integer I, the result is a square number. If 276 is added to to the same integer I, another square number is obtained. Find I.

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Answer:

I + 200 = A2 : 200 added to I (unknown integer) gives a square.

I + 276 = B2 : 276 added to I (unknown integer) gives another square.

B2 = A2 + 76 : eliminate I from the two equations.

add squares A2 (0, 1, 4, 9, 16, 25,...) to 76 till you obtain another square B2.

76 + 182 = 400 = 202

A2 = 182 and B2 = 202

I = A2 - 200 = 124

Step-by-step explanation:

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I = A2 - 200 = 124

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