MATLAB Answers

simplifying an algebraic expression in two variables

5 views (last 30 days)
hello
I know that
sqrt ((x-1)^2 + (y-2)^2) + sqrt ((x+1)^2 + (y+2)^2) = 6
and
8*(x^2) - 4*x*y + 5*(y^2) = 36
are equivalent, but is there a way of having matlab deduce the second statement from the first?
regards, Danny.

Accepted Answer

Tanmay Das
Tanmay Das on 6 Aug 2021
The following code may solve your problem:
clc;
clear ;
close all;
syms x y;
eqn = sqrt ((x-1)^2 + (y-2)^2) + sqrt ((x+1)^2 + (y+2)^2) == 6;
eqn1 = simplify(eqn^2);
eqn2 = expand(eqn1);
eqn3 = simplify(eqn2);
%As of now, MATLAB is not able to simplify expressions inside squre root by
%itself, so one needs to isolate it and then square both side
eqn4 = (x^2 - 2*x + y^2 - 4*y + 5)^(1/2)*(x^2 + 2*x + y^2 + 4*y + 5)^(1/2);
%isolating the square root term from rest of the equation
eqn5 = isolate(eqn3,eqn4);
%simplifying the equation
eqn6 = simplify(expand(eqn5^2));
%One can also solve the equation by executing the following line
sol = solve(eqn6,'ReturnConditions',true);
You can refer to the documentations on expand, simplify, isolate and solve functions for further information.

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!