 Hello and welcome to the session. Let us understand the following problem today. If a, b and c are real numbers and delta is equal to b plus c, c plus a, a plus b, c plus a, a plus b, b plus c, a plus b, b plus c and c plus a is equal to 0, shall add either a plus b plus c is equal to 0 or a is equal to b is equal to c. Now let us write the solution. We have delta is equal to b plus c, c plus a, a plus b, c plus a, a plus b, b plus c, a plus b, b plus c, c plus a equal to 0. Now applying r1 tends to r1 plus r2 plus r3. So we get it implies twice of a plus b plus c, twice of a plus b plus c, twice of a plus b plus c, c plus a, a plus b, b plus c, a plus b, b plus c, c plus a is equal to 0. Now taking common twice of a plus b plus c from the first row. So we get 1, 1, 1, c plus a, a plus b, b plus c, a plus b, b plus c, c plus a. This we have got by taking common twice of a plus b plus c from r1. Now applying this is equal to 0. So now applying c2 tends to c2 minus c1 and c3 tends to c3 minus c1. We will apply the column operation on column c2 and column c3. So we will get now which implies twice of a plus b plus c, 1, 0, 0. First column will be written as it is c plus a, a plus b. Now this here we get c2 minus c1, 1 minus 1 is 0 and a plus b minus c plus a will be equal to b minus c. Now similarly b plus c minus a plus b is equal to c minus a. Now column operation for column 3, 1 minus 1, 0 which we have written here, b plus c minus c plus a will be equal to b minus a and similarly c plus a minus a plus b is equal to c minus b which is equal to 0. Now solving it further we get twice of a plus b plus c multiplied by 1 into b minus c into c minus b minus c minus a into b minus a which implies twice of a plus b plus c is equal multiplied by now we get bc minus b square minus c square plus bc minus bc minus ac minus ab plus a square which is equal to 0. Now we get twice of a plus b plus c multiplied by bc minus b square minus c square plus bc minus bc plus ac plus ab minus a square equal to 0. Here we see that this bc gets cancelled with this bc so we are left with twice of a plus b plus c multiplied by bc plus ac plus ab minus a square minus b square minus c square is equal to 0. Now which implies either a plus b plus c is equal to 0 or bc plus ac plus ab minus a square minus b square minus c square is equal to 0. Now first let us consider this it implies bc plus ac plus ab is equal to a square plus b square plus c square and this is possible only if a is equal to b is equal to c thus a plus b plus c is equal to 0 or a is equal to b is equal to c hence proved. I hope you understood the problem. Bye and have a nice day.