Only 1% Got This Viral Math Olympiad Challenge! | Can You Solve It?

[00:00:01]Hello, you're welcome. How to solve this nice algebra problem to find the value of x here. Solution from here and what we have which is x / 3 or power 4 = 81.

[00:00:21]First step here this following we have a b^ n. This is same thing as a raised power b^ that is we can write this as x^ 4 over 3^ 4 = to 81 on this side.

[00:00:44]Then yeah multiply by 3^ 4* 3^ 4 mip 3^ 4 this here^ 4 cancel each other this give us x^ 4 = 81 * 3^ 4 and also x we can write 81 + 3 * 3 * 3 * 3 which is also 3^ 4.

[00:01:23]So this equation becomes x^ 4 = 3^ 4 * 3^ 4.

[00:01:34]Then when we apply the law of indices a power * b this is same as a * b^ n. So it means here that we can write this as x^ 4 = 3 * 3^ 4.

[00:01:54]So here we have x^ 4 = 3 * 3 that's 9^ 4 here.

[00:02:04]Then we take everything to one side as this x^ 4 - 9^ 4 = 0 here.

[00:02:16]The next step we can write 4 as 2 * 2.

[00:02:19]So this can be written as x² then r² - also 9² then r² equals to zero here. Then here this follows we have a square - b square which same thing as a + b into bracket into bracket a - b that is here a standing as x² b standing as 9 squ. [snorts] Then you can write this equation now as x² + 9² into brackets. Then bracket [clears throat] x² - 9² + bracket = 0 here.

[00:03:10]Then we have two cases from here. First one s² + 9² = 0. Then also we have s² - 9² = 0.

[00:03:27]Then solving here this horiz brackets into bracket a - bhat.

[00:03:43]Then here also what we have becomes x + 9 into bracket into bracket x - 9 close bracket = 0 here and [clears throat] also we have two cases here. First one x + 9 = 0 or we have x - 9 = to zero here.

[00:04:13]Then solving here we can write as x = - 9.

[00:04:22]This is a complex solution here. Then also here we have x = 9. This is also a complex solution here as we have two complex solutions from here.

[00:04:39]Then solving for the second case, this also follows when we have a square - b square. This same thing as a + b into bracket into bracket a - b.

[00:04:53]This here this becomes x + 9 into bracket into bracket x - 9 bracket = to zero here.

[00:05:07]Then also we have two cases here. First one x + 9 = 0 or we have x - 9 = 0 here. Then solving on this side this give us x = -9.

[00:05:27]This is a real solution here. And here also we have x = 9. This is also a real solution here.

[00:05:39]And therefore all together we have four solutions two and two complex.

[00:05:45]Then let's write everything together.

[00:05:48]Now that is we can start from the real solution we have x1 = 9 x2 = -9 x3 = 9 I which is complex and x4 = - 9. So we have these four solutions here.

[00:06:18]in this problem. Then let's check if this satisfy this given problem for the two solution which are x = + or - 9.

[00:06:33]When we substitute here this equation becomes plus or minus 9 all^ 4 over sorry we have plus or - 9 / 3 all 4^ 4 is it = 81 on this side then same thing as plus or minus 3 that's 3^ 4 is this = 81 on this side.

[00:07:07]Then plus or minus to power even number that's plus we have 3 to power 4 is equals to 81 on this side. Then here we can remove this plus then 3^ 4 that's 81 = to 81 here left hand side now equals to the right hand side and therefore these two solutions satisfy this given problem.

[00:07:38]Also we substitute the two complex solutions which are x = + or - 9.

[00:07:53]So this equation becomes plus or - 9 / 3 all^ 4.

[00:08:01]This is = 81 on this side.

[00:08:05]And then here you can write as plus or minus 9 3 that's 3^ 4 is it = 81 on this side then plus or minus power 4 is plus then yeah we have 3^ 4 * I^ 4 this is equals to 81 on this side we can remove the plus 3^ 4 is 81 * I^ 4 same thing as I² * I² and I square - 1 so - 1 * -1 that's 1^ 1 = 81 on this side 81 * 1 here give us 81 this = 81 here left hand side equals the right hand side and therefore we conclude that these two complex solutions also satisfy this given problem. Thank you for watching. Don't forget this step.

[00:09:09]Subscribe for more videos notification bell. Share this video. Give me a thumbs up. Put your comments. See you in next class. Bye for now.