 Hello and welcome to the session. In this session we discussed the following question which says if x is equal to square root 2p plus 3q plus square root 2p minus 3q upon square root 2p plus 3q minus square root 2p minus 3q, find the value of 3q x square minus 4px plus 3q. Now let's move on to the solution. We are given that x is equal to square root 2p plus 3q plus square root 2p minus 3q upon square root 2p plus 3q minus square root 2p minus 3q. Now we will rationalize the denominator of this x and for this we multiply its numerator and its denominator by square root 2p plus 3q plus square root 2p minus 3q upon square root 2p plus 3q plus square root 2p minus 3q. That is we get x would be equal to square root 2p plus 3q plus square root 2p minus 3q whole square and this total upon 2p plus 3q minus 2p minus 3q. So we get x is equal to 2p plus 3q plus 2p minus 3q plus 2 into square root of 2p plus 3q into 2p minus 3q and this total upon 2p plus 3q minus 2p plus 3q. We get x is equal to 2p plus 3q plus 2p minus 3q plus 2 square root of 4p square minus 9q square upon now 2p minus 2p cancels 3q plus 3q is 6q 3q minus 3q gets cancel we get x is equal to 4p plus 2 square root 4p square minus 9q square upon 6q. That is we have x is equal to 2p plus square root 4p square minus 9q square upon 3q. Now let's find out x square this is equal to 2p plus square root 4p square minus 9q square whole square upon 3q whole square that is we get x square is equal to 4p square plus 4p square minus 9q square plus 4p into square root of 4p square minus 9q square and this total upon 9q square. This further gives us x square is equal to 8p square minus 9q square plus 4p into square root 4p square minus 9q square and this total upon 9q square. So we now get the value for x square also. Now we need to find the value for 3q x square minus 4p x plus 3q. Now we have got the value for x square we now find the value for 3q x square this would be equal to 3q into 8p square minus 9q square plus 4p into square root 4p square minus 9q square upon 9q square. So this 1q cancels with 1q from here and 3 3 times is 9 so we get 3q x square is equal to 8p square minus 9q square plus 4p into square root of 4p square minus 9q square upon 3q. So this is the value for 3q x square now we find the value for 4p x this is equal to 4p into the value of x which is 2p plus square root 4p square minus 9q square upon 3q. So this gives us 4p x is equal to 8p square plus 4p into square root of 4p square minus 9q square upon 3q. So this is the value for 4p x now in this expression we substitute the values for 3q x square minus 4p x. So we have 3q x square minus 4p x plus 3q is equal to now the value for 3q x square is 8p square minus 9q square plus 4p into square root of 4p square minus 9q square upon 3q minus the value for 4p x which is 8p square plus 4p into square root of 4p square minus 9q square upon 3q plus 3q. This is equal to 8p square minus 9q square plus 4p into square root of 4p square minus 9q square minus 8p square minus 4p into square root of 4p square minus 9q square plus 9q square and this total upon 3q. Now 8p square minus 8p square cancels minus 9q square plus 9q square cancels 4p into square root of 4p square minus 9q square cancels with minus 4p square root of 4p square minus 9q square. So we get this is equal to 0 upon 3q which is equal to 0. So the value of the expression 3q x square minus 4p x plus 3q is equal to 0. So our final answer is 0. This completes the session. Hope you have understood the solutions for this question.