# Extract the x values that make the two functions values equal

I have two functions for the x variable. I want to extract x values that make the functions equal.

(1)

a + b - a b + c x - b c x + d x - a d x- a e x + a b e x- b f x + a b f x- c d x + a d e x + b c f x - a b e f x


(2)

a + b - a b + c x - b c x + d x - a d x - a e x + a b e x - b f x +
a b f x - c d x^2 + a d e x^2 + b c f x^2 - a b e f x^2


where $x\in[0,1]$ equal to each other (i.e. (1)=(2) )

Is it possible to make a program according to the structure of the functions in order to be equal according to the values of x?

A program that extracts x values in the form of a table that makes the functions equal. where $x\in[0,1]$

I need a program that prints 20 $x_i$ values in the form of a table with equal functions

variables = exp // Variables // Sort;

    exp = -Subscript[x, 3] Subscript[x, 4] Subscript[x, 5] Subscript[x, 6]
Subscript[x, 7] +
Subscript[x, 1] Subscript[x, 3] Subscript[x, 4] Subscript[x, 5]
Subscript[x, 6] Subscript[x, 7] +
Subscript[x, 2] Subscript[x, 3] Subscript[x, 4] Subscript[x, 5]
Subscript[x, 6] Subscript[x, 7] -
Subscript[x, 1] Subscript[x, 2] Subscript[x, 3] Subscript[x, 4]
Subscript[x, 5] Subscript[x, 6] Subscript[x, 7];

exper = -\!$$\*SubsuperscriptBox[\(x$$, $$3$$, $$2$$]\) Subscript[x, 4]
Subscript[x, 5] Subscript[x, 6] Subscript[x, 7] + Subscript[x, 1]
\!$$\*SubsuperscriptBox[\(x$$, $$3$$, $$2$$]\) Subscript[x, 4]
Subscript[x, 5] Subscript[x, 6] Subscript[x, 7] + Subscript[x, 2]
\!$$\*SubsuperscriptBox[\(x$$, $$3$$, $$2$$]\) Subscript[x, 4]
Subscript[x, 5] Subscript[x, 6] Subscript[x, 7] -
Subscript[x, 1] Subscript[x, 2]
\!$$\*SubsuperscriptBox[\(x$$, $$3$$, $$2$$]\) Subscript[x, 4]
Subscript[x, 5] Subscript[x, 6] Subscript[x, 7]


;

 Module[{expValue, experValue, varValues},
With[{nbrOfResults = 20},
Table[Catch[
Do[If[0.8 <= (expValue =
Round[exp /.
Round[RandomReal[{0, 1}, Length[variables]], .1])],
0.01]) < 1,
Throw[{NumberForm[#, {3, 1}] & /@ varValues,
NumberForm[expValue, {4, 5}],
NumberForm[
exper /. Thread[variables -> varValues], {4, 5}]} //
Flatten]], 10000]], {nbrOfResults}] //
SortBy[#, #[[-2]] &] &] //
Prepend[#, {variables, "exp", "exper"} // Flatten] & //
Grid[#, Frame -> All] &]


This program prints values of functions if they are larger than 0.5

I want to print values of variables if the functions are equal

• Have a look at Solve and NSolve. Jul 31, 2017 at 8:52

eqn1 = a + b - a b + c x - b c x + d x - a d x - a e x + a b e x -
b f x + a b f x - c d x + a d e x + b c f x - a b e f x ;

eqn2 = a + b - a b + c x - b c x + d x - a d x - a e x + a b e x -
b f x + a b f x - c d x^2 + a d e x^2 + b c f x^2 - a b e f x^2;

Solve[eqn1 == eqn2, x]

(* {{x -> 0}, {x -> 1}} *)


So either $x=0$ or $x=1$ (for all parameter values). The equations actually factorize, so you can see that these are the only solutions.

Simplify[eqn1 - eqn2]

(* (c - a e) (d - b f) (-1 + x) x == 0 *)

• I need a program that prints 100 X values in the form of a table with equal functions Jul 31, 2017 at 8:20