A Nice Math Olympiad Question

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[@TWJRPGGamming]

2^22-2=（2048^2）-2 = 4000000+192000 + 48^2 -2 = 4192000+2500-50*2*2 +4 -2= 4194302

[@theklaffs]

There's a much easier way to do this. 4^11= (2^2)^11= (2^11)^2= 2048^2= (2000+48)^2= (2000*2000)+(2*2000*48)+(48*48)= (2*2*1000000)+(96*2*1000)+(40+8)^2= (4000000)+(192000)+((40*40)+(2*40*8)+(8*8))= 4000000+192000+(1600+640+64)= 4192000+2304= 4194304 4194304-2=4194302

[@juergenilse3259]

When you add "-2+2" to the original expression, you get 2 added to the difference of 2 squares (2^11)^2-2^2+2), and you can use the identity a^2--b^2=(a+b)*(a-b) which is aso an easier way than that shown in the video

[@gediminasgudavicius1267]

I always pre-like your videos! Well done!😊

[@RyanLewis-Johnson-wq6xs]

4^11-2=4194302 It’s in my head.

[@kamleshchavan7451]

How did you solved in your head

[@juergenilse3259]

@@kamleshchavan7451 Maybe by knowing all powers of 2, at least up to 2^32 in his head. I do not know all theses powers of 2, but i know the powers of 2 up to 2^16, so i know 2^11=2048. With this in mind, i can use: 4^11-2= 4^11--4+2= (2^2)^11-2^2+2= (2^11)^2--2^+2= (2^11+2)*(2^11-2)+2= (2048+2)*(2048-2)+2= 2050*2046+2 which leads (at least in my opinion) to an easier calculation as shown in the video ....

[@imetroangola4943]

​@@juergenilse3259realmente é muito mais fácil do que o vídeo, deu até sono vê os cálculos longos, cansativos e desnecessários no vídeo mostrado.

[@lakshmikutty2255]

U are great!

[@kamleshchavan7451]

Any short solution

[@imetroangola4943]

4¹¹ - 2= (2¹¹)²- 2= (2¹¹)²- 1² -1= =(2¹¹+1)(2¹¹-1) -1= =2049×2047-1=4.194.303-1= = *4.194.302* Vídeo muito longo, cálculo cansativo e desnecessário!

[@EdwardBurgess-t7p]

Schneider Way

[@gaiatetuya92]

無駄な計算が多い。

[@reinhardtristaneugen9113]

I got 4 194 302 and I just calculated it by mental calculation... ...squared 4^5 what turns out to be 1048576, just to multiply it one last time by 4 and substract 2... ...not difficult at all... Le p'tit Daniel

[@shantasewnath3821]

Langabere!!!!!😊

[@juergenilse3259]

4^11--2= (2^2)^11-2^2+2= (2^11)^2-2^2+2= (2^11+2)*(2^11-2)+2= (2048+2)*(2048-2)+2= 2050*2046+2= 2050*(2000+40+6)+2= 4100000+82000+12300+2= 4182000+12300+2= 4194300+2= 4194302 Are you really shure, that your calculation is easier than mine?