 Hi and welcome to the session. Let's work out the following question. The question says the sum of two numbers a and b is 15 and the sum of their reciprocals 1 upon a and 1 upon b is 3 divided by 10. Find the numbers a and b. Let us start with the solution to this question. Now from the condition that the sum of two numbers a and b is 15, we have a plus b is equal to 15. We call this 1 and the sum of their reciprocals that is 1 by a plus 1 by b is given to be 3 divided by 10. So this implies that a plus b divided by a b is equal to 3 divided by 10. We call this equation 2. Now from equation 1 and equation 2 we have 15 divided by a b is equal to 3 divided by 10 because a plus b is equal to 15 or we can say that a b is equal to 15 multiplied by 10 divided by 3 and this is equal to 5 into 10 because 3 fives are 15. And we can say that a b is equal to 50 and we call this 3. Now we see that a plus b the whole square minus a minus b the whole square will be equal to a square plus b square plus 2 a b minus a square plus b square. Here we can have minus because positive sign with negative becomes negative. So a square minus b square plus 2 a b this is equal to now a square gets cancelled with minus a square and b square with minus b square. So we have 4 into a into b or we can say that 15 square minus a minus b the whole square is equal to 4 into 15 or 225 minus a minus b the whole square is equal to 200 or a minus b the whole square is equal to 200 or we can say 225 minus 200 or a minus b is equal to square root of 25 that is equal to 5. So a minus b is equal to 5 and we call this equation 4. Now adding equation 1 and equation 4 we have a plus b is equal to 15 plus a minus b is equal to 5. This gives us 2 a is equal to 20 or a is equal to 20 divided by 2 that is equal to 10. Therefore 10 plus b is equal to 15 this implies that b is equal to 15 minus 10 that is equal to 5. Therefore our answer to this question is a is equal to 10 and b is equal to 5. So I hope that you understood the solution and enjoyed the session. Have a good day.