Olympiad Mathematics | Can you solve this Japanese Math Olympiad Question?

[00:00:00]Hello everyone, welcome to Russa's classroom. Today we solve a easy math question. It is a seven get math question which is x + x + x / x * x * x = 1 x = 1. How to solve this interesting maths question? Our math solution our question which is x + x + x. and take our question. This is x + x + x over and this is x * x * x is equal to 1. This is our question. Now at this moment you can say here is x is common so it will be 1 + 1 + 1 so it will be 3.

[00:00:46]So 3x so you can say x + x + x it will be 3x over but this exponent is 1 this is 1 this is 1 so according to exponential formula it is basic same so 1 + 1 + 1 this is 3 so x * x * x it will be x ^ 3 is equal to 1 now at this moment I do here is cross multiplication so this is x cub * 1 this is x cq and is equal to and here is 1. So 1 * 3x this is 3x. So we find out it will be x cq is equal to 3x. This is a cubic equation. We are find out here is three solution three root in this exponential expression. So this is x cube and if I move on this value in this side it will be negative. So you can see that it will be - 3x is = 0. So we find out here is xq - 3x = 0.

[00:01:53]Then this is x cube this is x. So you can easily here is x is common. So if I take here is x is common. So this x cub / x this is x² minus this 3x / x it will be 3 is equal to zero.

[00:02:11]We are find out here is two case. Our first case which is x=0 and other case x² [clears throat] - 3 is equal to 0. So you can say here x = 0 and other case which is x ^ 2 - 3 = 0. Now you can move on this value in this side then you can use both side square root then we'll find out x equ= to + - <unk>3 or you can say here x² then 3 it will be square<unk> 3 bracket power is 2 is equal to z because of that I want to apply this identity here which is a square - b square it will be a + b * a - b so this is a + b time a minus b because of that we know that a² - b² which is a + b * a minus b I apply this math identity here then we find here is two case our first case x + <unk>3 is equal to zero and other's case x - <unk>3 is =0.

[00:03:30]But this is x = - <unk>3.

[00:03:35]This is x = + <unk>3. So this is cubic equation and we find out there is three solution. This is x=0. This is x= minus <unk>3. This is x = 3 <unk>3. So let's verify or let's check out our question.

[00:03:52]First of all, I take our answer which is x=0.

[00:03:56]X = <unk>3 and X= minus <unk>3. We are find our three solution.

[00:04:03]But I take our question which is X + X + X over this is X * X * X it will be 1.

[00:04:17]So let's verify. First of all I take our answer X is equal to Z. So if I take X is equal to Z. So at this moment you can say 0 + 0 + 0 and here 0 * 0 * 0 is equal to 1. So you can't say 0 cannot be equal 1. So I can't follow this value.

[00:04:38]This is rejected. It is not possible.

[00:04:41]But first of all we find out here x= <unk>3. So if I take at this moment x = <unk>3. This time you can say easily it will be square <unk>3 + <unk>3 + <unk>3 over this is square<unk> 3 * <unk>3 * <unk>3 uh is equal to 1. Is it right? Let's verify. So square <unk>3 is <unk>3 <unk>3 it will be 3 square <unk>3 and here <unk>3 * <unk>3 it will be three because of that square root is cancel like this is square <unk>3 * <unk>3 * <unk>3 which is <unk>3 bracket power is 2 * <unk>3 this this cancel it will be 3 <unk>3 so you go and say this time this time this it will be 3 square <unk>3 is equal to one. So this this cancel out we are find out here 1 is equal to 1. So left hand side and right hand side both side is equal. So you can say x is equal to <unk>3. This is our right answer.

[00:05:50]But at this moment x is equal to <unk>3.

[00:05:53]Is it right? Let's verify again. So at this moment you can say here I take minus <unk>3. So - <unk>3 + - <unk>3 + - <unk>3 over - <unk>3 * - <unk>3 * - <unk>3 this is one is it right? Let's verify.

[00:06:21]So here is left hand side minus <unk>3 this is minus <unk>3 this is minus <unk>3 so here is 3 - <unk>3 so you can see it will be 3 uh <unk>3 and this is minus yes this is minus and over uh this minus this minus it will be plus so <unk>3 * <unk>3 you know that it will be three so I take this three here but this is minus <unk>3 * 3 it will be minus square<unk> 3 is equal 1 but this this cancel it will be positive 1 is equal to positive 1. So left hand side and right hand side both side is equal. So you can say here x= minus² 3 it is also right answer in this exponential equation.

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