00:01
In this question, it is given that x1 square plus x2 square plus x3 square plus x4 square equals to 100.
00:12
Then x1 square should be less equals to 100.
00:19
Then x2 square should also be less equals to 100 and x3 square should be less equals to 100.
00:29
Similarly, x4 square should be less equals to 100.
00:34
So, this implies x1 should be less equals to 10 and greater equals to minus 10.
00:41
Similarly, x2 will be less equals to 10 and must be greater equals to minus 10.
00:49
Similarly, for x3, which should be less equals to 10 and greater equals to minus 10.
00:56
And x4, x4 should also be less equals to 10 and should greater equals to minus 10.
01:03
Now, since, since we want maximum value, since for maximum value, for maximum value of the equation, for the maximum value of equation x1, x2, x3, x4 can't be negative, otherwise it will not give the maximum value.
01:37
Therefore, x1, x2, x3, x4 should be less equals to 10 and they should be greater equals to 0.
01:52
So, now here the equation given is x1 plus 7 times of x2 plus 7 times of x3 plus x4.
02:06
Now, in this case, here x1 plus x4 plus 7 times of x2 plus x3.
02:15
So, x2 plus x3 should be maximum.
02:19
So, to get maximum value, maximum value x2 plus x3 must be maximum, must be maximum and the whole equation, the value of x1, x2, x3, x4 should satisfy this equation.
02:45
Now, if, if x2 equals to 7 and x3 equals to 7 and x1 equals to, x4 equals to 1.
03:00
So, therefore, x1 square plus x2 square plus x3 square plus x4 square, that is equals to square of x1 is, x1, x4 is 1.
03:16
So, square of 1 is 1 plus square of 1 is 1 plus square of 7 is 49 plus square of 7 is 49.
03:24
So, this is equals to 100.
03:25
That means, 1 of the value that will satisfy the equation is 7, 7.
03:30
Then next, if x2 equals to 8 and x3 equals to 4 and x1 equals to, x4 equals to 0.
03:42
Then x1 square plus x2 square plus x3 square plus x4 square will be, x1 square 0, x4 square 0 plus square of 8.
03:56
So, that will be equals to, here not 4, here it will be 6...