If a,b,c are the roots of x^3+4x+1=0 ,then the equation whose roots are a^2/(b+c) ,b^2/(a+c),c^2/(a+b) ?

a,b,c are roots

so we get comparing coefficients of x^2 ( that is sum of roots)

a+ b + c = 0 ..1
now
a^2/(b+c) ,b^2/(a+c),c^2/(b+a) are root of new equation

a^2/(b+c) = a^2/(-a) from (1)

so new equation has roots -a , -b , and -c

f(x) = x^3+4x + 1 = 0 has roots a,b,c

so f(-x) = - x^3 - 4x + 1 = 0 or x^3 + 4x -1 =0 has roots -a , -b , and -c ora^2/(b+c) ,b^2/(a+c),c^2/(b+a)