The equation x3 + 2x = 26 has a solution between 2 and 3. Use a trial and improvement method to find this solution. Give your answer correct to one decimal place.
+129839 x^3 + 2x - 26 = 0 let us guess that the root is 2.5
(2.5)^3 + 2(2.5) - 26 = -5.375 we kmow that the root must be between this and 3......add 3 + 2.5 and divide by 2 = 2.75
Let's test this (2.75)^3 + 2(2.75) - 26 = 0.296875 .....now we know that the root is between 2.5 and 2.75.....continuing the same process (2.5+ 2.75) / 2 = 2.625
(2.625)^3 + 2(2.625) - 26 = -2.662109375...and the root lies between this and 2.75
(2.625 + 2.75)/2 = 2.6875
(2.6875)^3 + 2(2.6875) - 26 = -1.214111328125 .....now we know that the root lies between 2.6875 and 2.75 ....so (2.6875 + 2.75) / 2 = 2.71875
(2.71875)^3 + 2(2.71875) -26 = -0.466583251953125.....and the root still lies between this and 2.75
(2.71875 + 2.75) /2 = 2.734375
(2.734375 )^3 + 2(2.734375) - 26 = -0.0868568420410156.....and the root still lies between this and 2.75
(2.734375 + 2.75)/ 2 = 2.7421875
(2.7421875)^3 + 2(2.7421875) - 26 = 0.1045069694519043.....and the root lies between this and 2.734375
(2.734375 + 2.7421875) / 2 = 2.73828125
(2.73828125)^3 + 2(2.73828125) - 26 = 0.0086997151374817...this is pretty close to 0.....
The actual root is about 2.737.......this is way more than the problem required...this just demonstrates that this process can be tedious...........
+129839 x^3 + 2x - 26 = 0 let us guess that the root is 2.5
(2.5)^3 + 2(2.5) - 26 = -5.375 we kmow that the root must be between this and 3......add 3 + 2.5 and divide by 2 = 2.75
Let's test this (2.75)^3 + 2(2.75) - 26 = 0.296875 .....now we know that the root is between 2.5 and 2.75.....continuing the same process (2.5+ 2.75) / 2 = 2.625
(2.625)^3 + 2(2.625) - 26 = -2.662109375...and the root lies between this and 2.75
(2.625 + 2.75)/2 = 2.6875
(2.6875)^3 + 2(2.6875) - 26 = -1.214111328125 .....now we know that the root lies between 2.6875 and 2.75 ....so (2.6875 + 2.75) / 2 = 2.71875
(2.71875)^3 + 2(2.71875) -26 = -0.466583251953125.....and the root still lies between this and 2.75
(2.71875 + 2.75) /2 = 2.734375
(2.734375 )^3 + 2(2.734375) - 26 = -0.0868568420410156.....and the root still lies between this and 2.75
(2.734375 + 2.75)/ 2 = 2.7421875
(2.7421875)^3 + 2(2.7421875) - 26 = 0.1045069694519043.....and the root lies between this and 2.734375
(2.734375 + 2.7421875) / 2 = 2.73828125
(2.73828125)^3 + 2(2.73828125) - 26 = 0.0086997151374817...this is pretty close to 0.....
The actual root is about 2.737.......this is way more than the problem required...this just demonstrates that this process can be tedious...........
