 Hello and welcome to the session. I am Asha and I am going to help you with the following question which says, find A if the coefficients of x square and x cube in the expansion of 3 plus Ax raise to the power 9 are equal. Let us now begin with the solution and the general term as dr plus 1 of this expansion is given by 9 cr into 3 raise to the power 9 minus r into Ax raise to the power r which is already equal to 9 cr 3 raise to the power n minus r into A raise to the power r into x raise to the power r. Now we are given that the coefficients of x square and x cube are equal. So first putting r is equal to 2 then we get the coefficient of x square which is equal to 9 c2 into 3 raise to the power 9 minus 2 into A raise to the power 2 which is further equal to factorial 9 upon factorial 2 into factorial 9 minus 2 that is 7 factorial into 3 raise to the power 7 into A square which is further equal to 9 factorial less 9 into 8 into 7 factorial upon 2 factorial less 2 into 1 which is 2 into 7 factorial into 3 raise to the power 7 into A square which is further equal to 2 4 z 7 factorial cancels out with 7 and 9 is 3 square and 3 square into 3 raise to the power 7 is 3 raise to the power 9. So we have 4 into 3 raise to the power 9 into A square. Now putting r is equal to 3 we get the coefficient of x cube which is equal to 9 c3 into 3 raise to the power 9 minus 3 into A raise to the power 3 which is further equal to factorial 9 upon factorial 3 into factorial 6 into 3 raise to the power 6 into A cube which is further equal to 9 into 8 into 7 into 6 factorial upon 3 factorial is 3 into 2 into 6 factorial into 3 raise to the power 6 into A cube which is further equal to 6 factorial cancels out with 6 2 4 z 8 and 3 into 3 raise 9 so we have 7 factorial 28 into 3 raise to the power 1 into 3 raise to the power 6 is 3 raise to the power 7 into A cube thus we have got the coefficient of x square is equal to 4 into 3 raise to the power 9 into A square and coefficient of x cube is equal to 28 into 3 raise to the power 7 into A cube. So let this be equation number 1 and this be 2. So as we are given that coefficient of x square is equal to coefficient of x cube so this implies 4 into 3 raise to the power 9 into A square is equal to 28 into 3 raise to the power 7 into A cube or A cube upon A square is equal to 4 into 3 raise to the power 9 upon 28 into 3 raise to the power 7 A square cancels out with A cube and we are left with A only and on the right hand side 4 into 7 is 28 and 3 raise to the power 7 cancels out with 3 raise to the power 9 and we are left with 3 raise to the power 2 so we have 9 upon 7 hence the value of A is 9 upon 7 so this completes the session take care and have a good day.