 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says show that the statement P that is if X is a real number such that XQ plus 4X is equal to 0 then X is 0 is true by method of contradiction by contradiction to show the validity of the statement say P. We assume that P is not true that is P is not true is true then we arrive at some result which contradicts our assumption therefore we conclude that P is true. This is how we find the solution to this question so this becomes our key idea for this question. Now we can start with the solution to this question if possible first of all let X be not equal to 0. Now we are given that XQ plus 4X equals to 0 where X belongs to real numbers or we can simply say that X is a real number. Now XQ plus 4X equals to 0 implies that X into X square plus 4 equals to 0 so either X is equal to 0 or X square plus 4 equals to 0 but X is not equal to 0 by the assumption therefore we say that X square plus 4 equals to 0 which implies that X square equals to minus 4 which is not possible X is a real number. Hence our assumption is wrong therefore X is equal to 0 and therefore statement true. So this is what we were supposed to prove in this question I hope that you understood the question and enjoyed the session have a good day.