Harvard University Entrance Exam Question | Can you solve ?

Ajouté : 2026-05-05

[00:00:00]Hello, welcome back once again. Today we have this interesting math problem from Harvard University. x^2 - x + 1 = 0.

[00:00:09]Here we're going to evaluate this ugly looking expression. Are you thinking of solving this quadratic equation for x?

[00:00:16]That is not the best way because the solutions here when you raise it to the power of 99999 that is going to be strange and you need a calculating device right so what do we do now let's bring down this equation that is x^2 - x + 1 = 0. Now let's multiply both sides by x. we get x into brackets x^2 - x + 1. This is equal to x * 0. Right?

[00:00:56]So open up the bracket to get x cubed - x^2 + x is = 0. So call this equation one and call this one equation two. Now let us add both equations. So starting from the left hand side we have x^2 - x + 1 + x cubed - x^2 + x from the right hand side 0 + 0. Now here this and this get cancelled. This and this get cancelled. So we are left with x cubed + 1 which is equal to z.

[00:01:43]Subtract one from both sides to get x cubed is equal to -1. Awesome.

[00:01:51]Now the expression the ugly looking expression where x to evaluate x to the^ 9 9 - 1 all over x ^ 99 999.

[00:02:08]So this is going to be equal to here we know it is a multiple of three. So x cub raised to the^ of okay that is going to be 3 3 right. So 3 3 3 3 3 then - 1 all over. So here x cub rais^ of 3 3 3 3 3.

[00:02:30]So here so it is going to be equal to x cub is -1. So we get -1 raised to the^ of 3 3 3 3 3 3 3 3 3 3 3 then - 1 all over -1 rais^ of 3 3 3 3.

[00:02:48]So the power is odd. So it's going to give us 1. So we get this is equal to -1 - 1 all over -1 which is equal to -1.

[00:03:00]Then - * minus here is + 1. which is equal to zero. So 0 is our correct answer. Thank you for watching. If you enjoyed the video, please kindly subscribe to this channel. Also like, comment and share.