No, I don't think that works. We know that
Letting and yields a root that we already know...
for example, there is a function f(x)= x^{3}+ax^{2}+bx+c=0 with roots Q,W,E
then teachers told me that by substituting y=x^{2} , then we can find out f(y)=0 s.t. it has roots Q^{2},W^{2},E^{2 }but why such substition can help us to find out equations with root Q^{2},W^{2},E^{2}? What are the reasons behind?
Thanks for your kind helpings
oh, i mean by sub. y=x^{2}, then x^{3}+ax^{2}+bx+c = 0 becomes
x(x^{2}+b) = -(a^{2}+c)
x(y+b)=-(ay+c)
x^{2}(y+b)^{2}=(ay+c)^{2}
y(y^{2}+2by+b^{2}) = (a^{2}y^{2}+2acy+c^{2})
y^{3}+2by^{2}+b^{2}y = a^{2}y^{2} + 2acy + c^{2}
y^{3}+y^{2}(2b-a^{2})+y(b^{2}-2ac)-c^{2} =0
then eqaution y^{3}+y^{2}(2b-a^{2})+y(b^{2}-2ac)-c^{2} =0, has required root, sorry for the misleading of using same function notication