00:01
I here for the given question, we are given that e to the power of 5 minus 81 d multiplied with d square minus 8 d plus 20 multiplied with d square plus 21 whole cube y is equal to 0.
00:21
So here in our case now, we need to solve this equation.
00:24
So further now, we know that here in our case, first of all, we will evaluate each term.
00:31
So here for d to the power 5 minus 81 d equals to 0 here.
00:37
We can say that we have value of d d multiplied with d to the power 4 minus 81 is equal to 0 on simplifying this.
00:46
We have value of d equals to d square whole square minus 9 square is equal to 0 this gives here.
00:57
We have d square minus 9 multiplied with d square plus 9 is equal to 0.
01:02
So here on simplifying this we have d square minus 9 can be written as d minus 3 multiplied with d plus 3 multiplied with d square plus 9 is equal to 0.
01:14
Now considering this d also here equals to 0.
01:18
So here we can say that now on solving this we have value of d equals to 3 minus 3 9 iota.
01:26
It will be 3 iota plus or minus 3 iota square.
01:31
So here we have value to be equal to plus 3 iota.
01:42
Similarly minus 3 iota and 0 now solving for d square minus 8 d plus 20.
01:49
So here in our case now on solving this further we can write this as d equals to minus minus plus 8 divided plus or minus under root of 64 minus 4 multiplied with 20 divided by 2.
02:06
So here now on simplifying this we can say that here we have value of d equals to 8 plus or minus under root of minus 16 upon 2.
02:16
So this is equal to 8 plus or minus 4 iota upon 2.
02:22
So simplifying this we have d equals to 4 plus or minus 2 iota.
02:27
So here these are the two roots...