Solving a 'Harvard' University entrance exam question

Hello friends, find the value of a if a plus 11 equal to a. Let's have a solution. If you see, a plus 11 equal to a, then a minus a will be equal to minus 11. a minus a is zero, which does not equal to minus 11. We have a question here, a plus 11 equal to a. To solve this, take square on both sides, which is same as a plus 11 times a plus 11 equal to a square. Simplify this, a times a, a square plus 11a plus 11a plus 11 times 11 equal to a square. a square on left hand side will be here, minus a square plus 11a plus 11a will be here, 22a plus 11 times 11 is 121 equal to zero. Where a square cancels, we have 22a plus 121 equal to zero. 22a equal to minus 121. To find a, divide by 22 on both sides, 22 cancels, 11 times 2 is 22, 11 times 11 is 121, a equal to minus 11 over 2. Suppose that, a plus 11 equal to a, put the value of a, minus 11 over 2 plus 11 equal to minus 11 over 2. Take LCM, we have minus 11 plus 11 times 2 is 22, equal to minus 11 over 2. Next we have a, 22 minus 11 will be here, 11 over 2, which does not equal to minus 11 over 2. But why? As x equal to y, x square equal to y square and also absolute value of x equal to absolute value of y, then we should take modulus on both sides. By this, we get 11 over 2, which is equal to 11 over 2. Thanks for watching this video. Please subscribe this channel to get the notification of my new videos. Ok Bye.