Single Copy $5: Fill & Download for Free

This is an exercise in keeping it simple.Proof: begin with a classical observation that for any two real numbers [math]x_1, x_2[/math] it is the case that:[math]\left(x_1 - x_2\right)^2 \geqslant 0 \tag{1}[/math]where the equality holds if and only if [math]x_1 = x_2[/math] and from where it follows that:[math]x_1^2 + x_2^2 \geqslant 2x_1x_2 \tag{2}[/math]If the real numbers [math]x_1[/math] and [math]x_2[/math] are positive, of which we are assured by the problem statement, then dividing both sides of (2) by the product [math]x_1x_2[/math], we get:[math]\dfrac{x_1}{x_2} + \dfrac{x_2}{x_1} \geqslant 2 \tag{3}[/math]As proof generators we are free to choose with which particular values to animate our numbers [math]x_1[/math] and [math]x_2[/math]. We choose these: [math]x_1 = \sqrt{a}[/math] and [math]x_2 = \sqrt{b}[/math]:[math]\dfrac{\sqrt{a}}{\sqrt{b}} + \dfrac{\sqrt{b}}{\sqrt{a}} \geqslant 2 \tag{4}[/math]Multiplying both sides of (4) by a single copy of a strictly positive real number [math]\sqrt{a}[/math]:[math]\dfrac{a}{\sqrt{b}} + \sqrt{b} \geqslant 2\sqrt{a} \tag{5}[/math]then, multiplying both sides of (4) by a single copy of a strictly positive real number [math]\sqrt{b}[/math]:[math]\sqrt{a} + \dfrac{b}{\sqrt{a}} \geqslant 2\sqrt{b} \tag{6}[/math]and adding (5) and (6) together:[math]\dfrac{a}{\sqrt{b}} + \dfrac{b}{\sqrt{a}} + \sqrt{a} + \sqrt{b} \geqslant 2\cdot\left(\sqrt{a} + \sqrt{b}\right) \tag{7}[/math]we, after canceling one copy of [math]\left(\sqrt{a} + \sqrt{b}\right)[/math] on both sides of (7), see that the result follows:[math]\dfrac{a}{\sqrt{b}} + \dfrac{b}{\sqrt{a}} \geqslant \sqrt{a} + \sqrt{b} \tag{8}[/math]what was required to prove.[math]\blacksquare[/math]

1. Open StackOverFlow And See This,2. Git Conflict’s Going No Where, After Every Other Commit You See Conflict’s,3. IDE Not Working Properly -4. Using Quotes,Single Quotes vs. Exactly Looking Like Single Quotes (But It’s Not)Double Quotes vs. Exactly Looking Like Double Quotes (But It’s Not)Happen’s When Copying From Some Other Source. (Yes I Copy)5. "Code Is Working, Don’t Know Why?"6. Error/Bug On Friday Evening.7. Error On Demo Day, Because You Tried To Change Something To Make It Better.8. No Documentation (Bad Documentation Is Nothing Better)9. Reading Your Old Previous Written Code And Asking “Who Wrote it?”10. Realizing Other Language Can Do Same Task With More Efficiency And Less Lines Of Codes. (No I Am Not Giving Example, There Are Lot Of Fans For Every Language And I Need Upvotes :P)

It happened few years back during my college days.Pic credit : GoogleI was new in Krishna Consciousness. It was December. I was distributing Bhagavad Gita. I was near railway station. I had a bag full of Bhagavad Gita. I spent almost more than 2 hours outside the railway station but could distribute only few books. I decided to go inside railway station. Response was good. I was very enthusiastic. I was approaching anyone and everyone. I still remember how I approached a Japanese couple and they said that they were atheist. I didn’t mind and continued showing Bhagavad Gita to the people.Suddenly I realized a group of 4 police officers along with some railway officials coming towards me. Before I could escape, they caught me. They asked me what was I doing? I honestly said that I was distributing Gita. I could have spoken something else, I could have given some excuse. But I decided to speak truth. They took me in their office. One police man told me that other book sellers who had license, complained about me. Probably they considered me their competitor.Main person was inside only and I was waiting for him to call me inside. They asked me the reason to sell Bhagavad Gita. I told them about Gita Marathon and importance of reading Bhagavad Gita.After few minutes, I was called inside and heavily chastised by that officer. I was speechless. He said “Why are you wasting your life doing all this. why do not you go and study? Why are you carrying Bhagavad Gita more heavier than your weight?( I was quite skinny those days -:))I just said one line “It gives me happiness”.He did not spoke anything for few minutes. Then the gentleman asked me, “How many copies of Gita do you have?” I said 7. He again thought for a while and then said something which I can never forget. He said, “ What if I take all the seven copies? Will you come again? I said, “No, I won’t come.” He took 5 or 6 copies of Bhagavad Gita. It was unexpected. I had never thought that he would take even a single copy. But Parmatma with in his heart inspired him.And at the end he smiled and said, “I know what you are doing is right but there are some rules which we can’t break”. I thanked him and came back.Truth works.