Question

$\pink{༄QuestioN}$
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 1

❍ Given : 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.

❍ To Find : Find I.

✬ Solution :-

❒ The two square numbers are :-

• x² and y² .

☯ x² and y² must differ by,

• 276 − 200 = 76 .

☯ Thus, assuming,

• x>y

☯ we have ,

• x2−y2 = 76 , or (x+y)(x−y) = 76.

❒ Since, x+y and x−y are both positive integers, we have three options :-

• x+y = 19 ; x−y =v4;
• x+y = 38 ; x−y = 2;
• x+y = 76 ; x−y = 1.

➯ The first and third options are dismissed since x and y wouldn’t be integers. The second option yields x = 20,y = 18 . So we have I = 182−200 = 124 . Alternatively, I = 202−276 = 124 .

✬ Hope it helps u ✬

Answer 2

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

hope it's help you ☺️☺️☺️☺️

but aasay Kyu only mods stars are allowed to answer but why????