Iterative process help gcse level

ITERATIVE PROCESS IN "EQUATIONS AND GRAPHS"

I'm familiar with questions with x on the LHS and a square root on the RHS.
This is the question structrure im stuck with:

12c) y=x2 - x - 3 x= 3/ x - 1 x0 = -1.5

What don't you understand? Is it the rearrangement or how to use your calculator to produce $x_1$ , $x_2$ etc?

usually, im familiar with x on the LHS and a root on the RHS, but as you can see there is no root but a fraction? I am struggling to understand where you'd put the 'n+1' and 'n'


Thankyou for your time

You put the n+1 on the left and the n on the right.

I'll rearrange this for you.

$x^2-x-3=0$

Add 3 to each side.

$x^2-x=3$

Factorise left hand side.

$x(x-1)=3$

Divide both sides by $x-1$.

$\displaystyle x=\frac{3}{x-1}$

Now add the n+1 and n.

$\displaystyle x_{n+1} = \frac{3}{x_n -1}$

Do you know how to use your calculator to do the rest?

yeah, I'm good with the repetitive using the previous answer to make a new result. How come you factorised the LHS?

The purpose was to form a product with x multiplied by something so that we could divide by the something.

If you are wondering why we don't always square root, the reason is that some iterative formulas don't work so we sometimes have to be clever about finding a different rearrangement that will work.