Ask Your Question

# polynomial equation

How can I solve it by sage?

Sage: solve(-6-4*y-x-(1+y)*x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2)==0, (2*(4+2*y+x))*(1+y)-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2)-(2+y)*(-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2))==0, x,y)

edit retag close merge delete

## 2 Answers

Sort by ยป oldest newest most voted
var('x y')
eq1 = -6-4*y-x-(1+y)*x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2)==0
eq2 = (2*(4+2*y+x))*(1+y)-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2)-(2+y)*(-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2))==0
show(eq1)
eq11 = eq1 + 6 +x*(y+1) + x + 4*y
eq12 =(eq11^2).expand()
show(eq12)
eq13 = eq12 - eq12.lhs()
show(eq13)
print '------------'
show(eq2)
eq21 = eq2.simplify_full()
show(eq21)
eq22 = eq21 - 6 -2*x -(x+4)*y^2 -(3*x+10)*y
show(eq22)
eq23 = (eq22^2).expand()
show(eq23)
eq24 = eq23 - eq23.lhs()
show(eq24)

more

It is not clear in your question on which field or ring you want to solve your equation. Though the following sequence of computations seems to indicate that your system is verified by any value for x and y:

sage: var('x,y')
(x, y)
sage: p = -6-4*y-x-(1+y)*x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2)
sage: q = (2*(4+2*y+x))*(1+y)-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2)-(2+y)*(-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2))
sage: s = solve(p==0,x,y); s
([x == -(4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)/(y + 2)],
[1])
sage: x0 = s[0][0].rhs()
sage: q.subs(x=x0)
-((4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)*(y + 1)/(y + 2) + sqrt(-4*(2*y - (4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)/(y + 2) + 4)*(y + 1)*((4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)/(y + 2) - 2) + ((4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)*(y + 1)/(y + 2) - (4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)/(y + 2) + 2)^2) - (4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)/(y + 2) + 2)*(y + 2) + 2*(2*y - (4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)/(y + 2) + 4)*(y + 1) + (4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)*(y + 1)/(y + 2) + sqrt(-4*(2*y - (4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)/(y + 2) + 4)*(y + 1)*((4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)/(y + 2) - 2) + ((4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4*x^2 + 4*(x^2 + 7*x + 12)*y + 24*x + 36) + 6)*(y + 1)/(y + 2) - (4*y - sqrt((x^2 + 8*x + 16)*y^2 + 4 ...
more

## Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

## Stats

Asked: 2016-01-13 16:00:32 +0200

Seen: 115 times

Last updated: Jan 14 '16