Question

the sum of the squares of two consecutive odd positive integers is 394 .find them​

Answer 1

Let the two consecutive odd numbers be x and x+2. ATQ, X2 + (X+2)2 = 394 X2 + X2 + 4X + 22 = 394 2X2 + 4X + 4 = 394      .......( dividing the equation by 2) X2 +2X =(394 - 4)/2 X2 + 2X = 195 X2 +2X - 195 = 0 X2 + 15X - 13X -195 = 0    .............( by factorization meathod ) X( X + 15 ) - 13( X + 15 ) = 0 ( X + 15 ) ( X - 13 ) X = -15 OR X = 13 CASE 1 If X = -15, then, X + 2 = - 13 CASE 2 If X = 13, then, X + 2 = 15