you're going to have to manipulate your equation "(1/32)*(n1*r1^2+n2 *r2^2+n3*r3^2) =1" so that it is solving for r1. using what you have for d1 = d2 = d3, you can solve for r2 and r3 in terms of r1. that makes manipulating the equation given so that "r1 = ......." easier. you can then input your work into matlab.
once you input your n1, n2, and n3 values into matlab, you can input the "r1 = ..." equation in to solve for r1. then to solve for r2 and r3, you just have to input the equations that you manipulated to solve for r2 and r3 in terms of r1.
see code below.
n1 = 4;
n2 = 8;
n3 = 16;
r1 = 32 / (n1 + n2*((sin(0.5*pi)/sin(pi/8))^2)+n3*((sin(0.5*pi)/sin(pi/16))^2))
r2 = r1*sin(0.5*pi)/sin(pi/8)
r3 = r1*sin(0.5*pi)/sin(pi/16)
hope this helped!
