Consider the following equations. f(x)=x³+3x²-x-6

g(x)=x²-3x-2

approximate the solution to the equation f(x)•g(x) using 3 iterations of successive application. use the graph as a starting point.

what is the appropriate value for the solution to the equation f(x)=g(x)?​

answer: 45

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584