Question

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

Answer 1

Answer:

The value of l is 124

124 + 200 = 324 = 18²

124 + 276 = 400 = 20²

Therefore, the number is 124.

Step-by-step explanation:

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Answer 2

The two square numbers x2 and y2 must differ by 276-200 = 76. Thus, assuming x>y.

We have, x2 - y2 = 76

( x+y )( x-y ) = 76

As x+y and x-y are both positive integers, we have:

i) x + y=19 ; x - y=4

ii)x + y=38; x - y=2

iii)x + y=76; x - y=1

The first and third options are not possible as x and y wouldn't be integers. The second option gives:

x = 20 ; y = 18

I = 18^2 - 200 = 124, alternatively

I = 20^2 - 276 = 124.

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