If 200 is added to a positive integer I, the result is a square number

1.	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.✔Only mods/stars are allowed to answer
Answer» <U>❍ 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 ✬

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.✔Only mods/stars are allowed to answer

Answer»

<U>❍ 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 .