Harvard University Admission Interview Tricks | Find the value of K=?

Added: 2026-05-31

[00:00:00]Hello, you are welcome to solve this math problem which is k^ 4 is equal to k - 4 bracket power 4. To find the values of k from this equation now in the first step here it will be k^ 4. We take this k - 4 bracket^ 4 to the left side. So it will be minus k - 4 bracket^ 4 is = 0.

[00:00:30]Then into here k^ 4 power 4 into squares. So it will be k^ 4 is same as 2 * 2 minus here also into squares. So here it will be k - 4 bracket^ of 4 is same as 2 * 2 is = 0.

[00:00:51]Then into here we take this k square inside the bracket. So it will be k² then bracket this square outside the bracket minus here k - 4 bracket square inside the bracket. So it will be k - 4 bracket square bracket this square outside the bracket is equal to zero. Now into here is now in the difference of two squares. So we'll apply difference of two square rule which is a square - b square is equal to a minus b bracket bracket a + b bracket.

[00:01:35]So here when you compare a square with k square bracket square then a is equal to this inside the bracket which is k².

[00:01:44]And here when you compare b square with k - 4 bracket square bracket square then b is equal to this here which is k - 4 bracket square then we apply this form a minus b it will be this minus this. So here it will be k² minus this here k - 4 bracket square then bracket here bracket a + b it will be this plus this. So here k² + k - 4 bracket² bracket is equal to this zero.

[00:02:31]Then into here it will be bracket this here which is k² minus we expand this so it will be bracket here it will be k² - 2 * k * 4 + 4 square bracket then bracket we close the bracket then here it will be k² + we expand this so here it will be k² square - 2 * k * 4 then plus this here 4² bracket is equal to zero then into here it will be bracket here k² - k² - 2 * 4 is 8 * k is 8 k + 4² it is 16 bracket Then bracket here k + k it is 2 k² then here - 2 * 4 is 8 8 * k is 8 k + 4² it is 16 bracket is equal to 0.

[00:03:50]Then here it will be bracket k² we open this inside the bracket inside bracket by negative. So it will be - k² minus and minus it will be + 8 k + sorry - and plus it will be - 16 bracket then here bracket 2 k² - 8 k + 16 bracket is equal to zero.

[00:04:23]Then into here k² - k² is 0. So this and this will cancel. Then we'll be left with this 8 k - 16 bracket. Then bracket 2 k² - 8 k + 16 bracket is equal to zero.

[00:04:45]Then into here we have two solutions where this first solution of 8 k - 16 is = 0 and this second solution of 2 k² - 8 k + 16 is = 0.

[00:05:03]Then into here we take -16 to the right side. So it will be 8 k is =6.

[00:05:11]Then into here we divide by 8 in both sides. So this and this will cancel.

[00:05:17]Then it will be k is equal to 16 / 8 it is two. So this is the first solution which is real solution.

[00:05:27]Then to solve from here we divide by two in both sides. So it will be 2 k² / 2 - 8 k / 2 + 16 / 2 is equal to 0 / 2.

[00:05:46]Now here 2k² / 2 it is k² - 8k / 2 it is 4 k + 16 / 2 it is 8 is equal to 0 / 2 it is 0.

[00:06:01]Then here to find the values of K we'll apply quadratic formula. So from quadratic formula which is K is equal to B + or minus square<unk> of B² - 4 A C over 2 A. Here coefficients A is equal to cofficient of K² is 1. B is equal to quotient of K is -4 and C is equal to constant it is 8.

[00:06:34]So here it will be k is equal to b is it is -4 then plus or minus square<unk> of b² it will be -4 bracket square then - 4 * a it is 1 * c is 8 then over [snorts] 2 * a it is 1 then into here it will be k is equal to -4 4 is pos4 + or minus square<unk> of -4 square is positive 16. Then -4 * 8 is - 32 over 2 * 1 it is 2.

[00:07:21]Then here it will be k is equal to 4 + or minus square<unk> of 16 - 32 here is - 16 over this 2. So into here it will be k is = 4 + or minus square<unk> of -16 is same as 16 * -1 then over this 2 then here it will be k is = 4 + or minus we separate the square root so it will be square root of 16 *<unk> of -1 / 2. So here it will be k is = 4 + or minus roo<unk> of 16 it is 4 roo<unk> of -1 it is i then divide by two here divide by two and into this side divide by two. So it will be k is = 4 / 2 it is 2 + or minus 4 i / 2 it is 2 i. So from here we have two complex solutions.

[00:08:32]Therefore our conclusion the first value of K is equal to which is real solution it is this two here the second value of K is equal to here when it is positive it is 2 + 2 I then the third value of K is equal to when it is negative it is 2 - 2 I so these are all the values of K from this our problem.

[00:09:04]Now in the next step let's check here this is real solution. These two here a complex solution.

[00:09:14]So here let's check uh as we check for real solution here k is 2. Now for my problem which is k^ 4 is equal to k - 4 bracket^ 4. So here let's check for k is = 2. Now here we substitute two here 2. So it will be 2^ 4 is it = 2 - 4 bracket^ 4. Now 2^ 4 it is 16. Is it = 2 - 4 is -2 bracket^ 4?

[00:09:57]Then here to be 16 is it equal to negative power of power of even number is positive. So 2^ 4 it is positive 16.

[00:10:08]So left side and right side are equal or from here sum will solve in this way from k^ of 4 is equal to k - 4 bracket^ 4. So we'll cancel this power four cancel this power four but here when you cancel this K it should be between absolute is equal to K - 4 here should be absolute.

[00:10:39]So here when it is positive positive here it is positive or here when it is positive it is negative when it is between absolute it should be positive. Example here when it is -2 it is -2 between absolute is equal to this here k is -2 then -4 absolute here here it will be pos2 is = here -2 -2 is -6 absolute this here it when it is between absolute to be positive. So it will be 6 is equal to 2 but it's not equal. So this is wrong.

[00:11:29]Now when we substitute our answer which we check here it is k it is two here it will be we substitute two inside the absolute. So it will be 2 absolute is equal to here 2 - 4. So 2 - 4 absolute.

[00:11:49]So here it will be 2 absolute is = 2 - 4 is -2 absolute. Now here when it is positive it will be positive. So it will be positive2 is equal to -2 when it is negative inside the absolute it will be positive. So here it will be two. So left side and right side are equal. But this here is not the correct solution.

[00:12:17]The only solution is what you did until here. So we have four three solutions.

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[00:12:35]Bye-bye.