00:01
Hi, in this question we will start with the given equation that is x q plus 2x is equal to 1.
00:08
So we will start with letting the function fx to be equals to x q plus 2x minus 1.
00:16
So first we check for f of 0 that is equals to minus 1 which is less than 0.
00:22
Then we check for f of 1 that is equals to 1 plus 2 minus 1 that is equal to 2 which is greater than 0.
00:29
So, fx is continuous on an interval from 0 to 1 as we can see.
00:39
Now, the root of equation will lies in this interval only.
00:44
For the first approximation, we can see x0 to be equals to a plus b by 2.
00:53
That is equals to 0 plus 1 by 2.
00:57
That is equals to 0 .5.
00:59
So we can find the function f at 0 .5 that is equals to 0 .5 raise to part 3 plus 2 times 0 .5 minus 1.
01:13
And solving this we get the result to be equals to 0 .1 to 5.
01:19
Now for the second iteration because this is greater than 0...