The equaltion given below has 4 roots. I only want to see the 2nd solution for each alpha and it will come in a list. I don't want to see all the solutions. What to do

for alpha from .4 by .1 to 5 do
S := solve(x^4-alpha, x);
S[2] ;
end do;

By a straight forward calculation, one can check that the expressions

(2*delta^2-2*beta*delta+alpha^2-2*alpha*delta+beta^2)*N^2+2*gamma*(beta+alpha-2*delta)*N+2*gamma^2

and 

(N*beta-N*delta+gamma)^2+(N*(alpha-delta)+gamma)^2

are same and equal. 

How to get the 2nd expression from the 1st expression by simplification by using MAPLE. 

I have the following expression 

lambda1-2.9881355172134833*lambda2+16.044692204509636*lambda1^2-114.31727386075951*lambda1*lambda2+202.36051939112247*lambda2^2

I want to get the expression in a form in which all the coeffs are fixed to 7 decimal places. 

I have tried with 

evalf[7](lambda1-2.9881355172134833*lambda2+16.044692204509636*lambda1^2-114.31727386075951*lambda1*lambda2+202.36051939112247*lambda2^2)

I have a 2D ode system. Let the interior equilibrium points be x1 & y1. It is easy to get the Jacobian matrix with the code

> with(linalg);
> with(DEtools);
> J := jacobian([H, K], [x, y]);

where H & K are the RHS of odes. But I need the higher order terms by transforming x=x1+u, 

y=y1+v in matrix notation. Please give me the code.