 Hello and welcome to the session. In this session we discussed the following question which says the sum of the squares of two consecutive odd numbers is 394, find the numbers. Let's proceed with the solution. We need to find two consecutive odd numbers. The sum of whose squares is 394. So, we take let the two consecutive odd numbers be x and x plus 2. So, now, into the question we have that x square plus x plus 2 the whole square is equal to 394. So, further we get x square plus x square plus 4x plus 4 is equal to 394. This gives us 2x square plus 4x plus 4 minus 394 is equal to 0. That is we have 2x square plus 4x minus 390 is equal to 0. Now, taking two common from the left hand side we have inside the bracket x square plus 2x minus 195 is equal to 0. This gives us x square plus 2x minus 195 is equal to 0. Now, splitting the middle term we get x square plus 15x minus 13x minus 195 is equal to 0. This gives us x into x plus 15 the whole minus 13 into x plus 15 the whole is equal to 0. That is x plus 15 the whole multiplied by x minus 13 is equal to 0. This gives us x plus 15 equal to 0 or x minus 13 equal to 0. That is x is equal to minus 15 or x is equal to 13. So, now first when we take x equal to minus 15 the two consecutive odd numbers that is minus 15 and x plus 2 that is minus 15 plus 2 that is minus 15 and minus 13 are the two consecutive odd numbers when x is equal to minus 15. Now, next when we take x equal to 13 the two consecutive odd numbers are x that is 13 and x plus 2 that is 13 plus 2 that is the two consecutive odd numbers are 13 and 15. So, when x is equal to 13 the two consecutive odd numbers are 13 and 15. This completes the session hope you have understood the solution of this question.