The German Math Olympiad Problem That 99% of Students Get Wrong!

Added: 2026-05-23

[00:00:00]Welcome to smart math. Today I'm trying to solve this math problem with a very unique way. So, as our equation is I am wrote here 1 + x divided by x + 1 that is equals to 2.

[00:00:15]This mean if I'm the reverse this equation x + 1 divided by x + 1 that is equals to 2 means this term and this term same and canceled out. This mean 1 is equals to 2.

[00:00:29]So, this is not possible. It It just for fun. So, if this situation exists, so which method try to solve this equation?

[00:00:41]So, let's find out the solution. So, if this if this situation exists So, if I'm wrote main equation 1 + x divided by by x + 1 that is equals to let's suppose that is equals to 2.

[00:00:58]So, this is if I'm trying to multiply this is division term goes equal opposite side mean multiplication here.

[00:01:05]So, equation become 1 + x that is equals to 2 into x + 1 here.

[00:01:14]So, now multiply inside. Equation is 1 + x that is equals to 2 into x is 2x + 2 into 1 is 2.

[00:01:26]So, further if I'm trying to solve this is positive This is positive go goes equal opposite side sign mean negative. This is positive goes equal opposite side mean negative. So, equation is 1 - 2 2x - x here.

[00:01:43]So, x is equal to -1 here.

[00:01:49]So, this mean the value of x that is equals to -1.

[00:01:54]The value of x that is I mean equals to minus one.

[00:01:57]So if I'm further in another method used.

[00:02:01]Let's suppose our equation is one x one plus x.

[00:02:05]Here.

[00:02:06]Or.

[00:02:07]Two of x.

[00:02:09]Plus one here.

[00:02:11]Two two into x plus one here. So if I'm trying to solve this.

[00:02:15]I'm trying to solve.

[00:02:17]I get to both side by squaring method.

[00:02:20]Both side by squaring method. So this equation become.

[00:02:23]One.

[00:02:25]Plus.

[00:02:27]One value and one plus x into one value.

[00:02:30]So this is also equation. Two into x is.

[00:02:34]That is equals to.

[00:02:37]Two of x plus two into one is two.

[00:02:41]That is two square. So if I'm wrote this equation is also two of x plus two.

[00:02:47]One or two of x plus two.

[00:02:50]Into one. So one.

[00:02:54]Plus x.

[00:02:55]Into one plus x here.

[00:02:58]So if I'm further solve if I'm further solve one into one plus x here and plus x.

[00:03:05]One plus x here.

[00:03:07]So that is equals to.

[00:03:09]This will be also equals two into two.

[00:03:12]X here multiplied by these two term two x.

[00:03:16]Plus two.

[00:03:17]And plus two here.

[00:03:19]Two x.

[00:03:20]Plus two.

[00:03:22]So one into one is become.

[00:03:25]Our equation become one into one is one plus one into x is x.

[00:03:31]Plus one into.

[00:03:34]X into one is x and x into x is x square.

[00:03:38]That is equals.

[00:03:40]Two into two is four x into x is x square plus two into two is four and x here.

[00:03:47]So one two into two is four and x here and two into two into and two is four here.

[00:03:55]So now for the next step is 1 + X into X is two of X plus X squared that is equal to 4 X squared plus 4 into 4 is become 8 X plus 4.

[00:04:10]So if I'm reverse this equation, the equation look like 4 X squared plus 8 X plus 4 that is equal to X squared here plus two of X plus one here.

[00:04:26]So this term is positive goes equal opposite side mean negative.

[00:04:31]So equation become 4 X squared 4 X squared minus X squared plus I'm trying to solve 8 X minus two of X plus 4 minus 1 that is equal to zero.

[00:04:49]So 4 minus 1 is 3 X squared and 6 minus 2 become 6 so 8 minus 2 is 6 X here. Plus 4 minus 1 become 3 that is equal to zero. So this is the quadratic equation. Now I'm trying to common 3 here.

[00:05:08]X squared plus two of X plus 1 that is equal to zero divided by by 3 here and divided by by 3 here. 3 3 cancel.

[00:05:18]So X squared plus two of X plus 1 that is equal to zero.

[00:05:26]So this is the the value of A squared the formula of A squared plus 2 A B plus B squared formula that is equal to A plus B whole squared.

[00:05:39]So now this become X minus So X this so this become X plus one whole square that is equals to zero. So taking square root here and and this is square root here. This is possible negative cancel one plus X plus one that is equals to zero. So this is positive you goes equal opposite side negative. So equal answer [snorts] is X is equals to minus one.

[00:06:11]Is the final answer.

[00:06:14]So I hope you will be fun. So thanks for watching. Keep like, share and subscribe.