Question

the equation
x^3+10x=25

has a solution between 1 and 2

use trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show ALL your working.

Answer 1

please could someone help me work this out!!:)

Answer 2

Well, they want you to use trial and error, so start with something like x = 1.5 and see if you need to go higher or lower.

Answer 3

When x = 1, 1^3 + 10(1) = 11 (too small)
When x = 2, 2^3 + 10(2) = 8 + 20 = 28 (too big)
Try x = 1.5, gives 18.375 (too small)
x is now between 1.5 and 2.
Now try x = 1.9, this gives 25.859 (slightly too big).
x = 1.8 gives 23.832 (slightly too small).
As 1.9 is nearer to the solution than 1.8, we say that the x-value satisfying this equation is 1.9 correct to 1 dp. I can clarify further if necessary. Hope this helps :)

Answer 4

so all i need to write down is this:

x = 1, 1^3 + 10(1) = 11 (too small)
x = 2, 2^3 + 10(2) = 8 + 20 = 28 (too big)
x = 1.5, gives 18.375 (too small)
x is now between 1.5 and 2.
x = 1.9, this gives 25.859 ( too big).
x = 1.8 gives 23.832 ( too small).
x=1.9

Answer 5

or do i write:

x = 1, 1^3 + 10(1) = 11 (too small)
x = 2, 2^3 + 10(2) = 8 + 20 = 28 (too big)
x = 1.5^3 + 10 = 18.375 (too small)
x = 1.9^3 + 10 = 25.859 ( too big).
x = 1.8^3 + 10 = 23.832 ( too small).
x=1.9

Answer 6

Probably better to write the latter as you need to show all working.

Answer 7

i dont understand how 1.5 = 18.375
and all of the others after this stage