Solving a system of equations, with for loop ?

Hell all :)

I'm a beginner on MatLab, and I have difficulties to solve "at once" this system of equations:

TSR=7.5;    %Tip Speed Ratio

%a
syms a1 a2 a3 a4 a5 a6 a7 a8 a9 a10
x=linspace(1,TSR,10)';
eqn1=(x(1)==(4*a1-1)*sqrt((1-a1)/(1-3*a1)));
eqn2=(x(2)==(4*a2-1)*sqrt((1-a2)/(1-3*a2)));
eqn3=(x(3)==(4*a3-1)*sqrt((1-a3)/(1-3*a3)));
eqn4=(x(4)==(4*a4-1)*sqrt((1-a4)/(1-3*a4)));
eqn5=(x(5)==(4*a5-1)*sqrt((1-a5)/(1-3*a5)));
eqn6=(x(6)==(4*a6-1)*sqrt((1-a6)/(1-3*a6)));
eqn7=(x(7)==(4*a7-1)*sqrt((1-a7)/(1-3*a7)));
eqn8=(x(8)==(4*a8-1)*sqrt((1-a8)/(1-3*a8)));
eqn9=(x(9)==(4*a9-1)*sqrt((1-a9)/(1-3*a9)));
eqn10=(x(10)==(4*a10-1)*sqrt((1-a10)/(1-3*a10)));
a1=vpasolve(eqn1,a1,[1/4 1/3]); %Finding a between 1/4 and 1/3
a2=vpasolve(eqn2,a2,[1/4 1/3]);
a3=vpasolve(eqn3,a3,[1/4 1/3]);
a4=vpasolve(eqn4,a4,[1/4 1/3]);
a5=vpasolve(eqn5,a5,[1/4 1/3]);
a6=vpasolve(eqn6,a6,[1/4 1/3]);
a7=vpasolve(eqn7,a7,[1/4 1/3]);
a8=vpasolve(eqn8,a8,[1/4 1/3]);
a9=vpasolve(eqn9,a9,[1/4 1/3]);
a10=vpasolve(eqn10,a10,[1/4 1/3]);
a=[a1;a2;a3;a4;a5;a6;a7;a8;a9;a10];

Indeed, it is very repetitive and if I have 100 variables to find I cannot think about typing all the equations one by one like I did here with 10. :/

I have thought about a for loop, but I cannot manage to make it work.

Thanks in advance for you help :)

Answer 1

[Alex Mcaulley]

This is an option:

TSR=7.5;    %Tip Speed Ratio
%a
syms aux
x=linspace(1,TSR,10)';
a = zeros(size(x));
for i = 1:numel(x)
    eqn = x(i)==(4*aux-1)*sqrt((1-aux)/(1-3*aux));
    a(i) = double(vpasolve(eqn,aux,[1/4 1/3]));
end

[Bertrand Canetti]

Great!

Big thanks again Alex. :)

Answer 2

[Nazer khan]

f1(x) = −20e−0.02qD−1PD i=1 x2 i −eD−1PD i=1 cos(2πxi) + 20 + e

matlab code for this