# How to use Solve

I have three quite complicated equations:

(-11+4t2-2t2^2-8t1t2(-1+[Lambda])+28[Lambda]+4t2[Lambda]+8t2^2[Lambda]+4t1(-2+(4+2t1t2+t2)[Lambda])/(2(1+t1)^3))==0

(-1+t2+(2+6t1+4t1^2)[Lambda]-4t2[Lambda])/((1+t1)^2)==0

(-57+16t2-16t2^2+t1^2(31+32t2)+t1(-2-32t1t2+48t2)/(8(1+t1)^2))==0

And I would like to solve them for the variables t1,t2 and lambda

I tried to insert the equations in ''Solve'', but I incurred in a syntax problem

I tried to insert the equations in ''Solve'', but I incurred in a syntax problem

it looks like you have problem with spaces. t1t2 is not the same as t1 t2. That is why I use explicit * myself between symbols. It might not make the code look as nice, but it can save time in debugging. But this should not have given you a syntax error. You might have a syntax error when you used the command Solve itself, which you did not show.

Any way, I rewrote everything from scratch and now it works.

ClearAll[t1, t2, λ]
eq1 = (-11 + 4*t2 - 2*t2^2 - 8 t1*t2 (-1 + λ) + 28*λ + 4*t2* λ + 8*t2^2 *λ + 4*t1 (-2 + (4 + 2*t1*t2 + t2)*λ)/(2*(1 + t1)^3)) == 0
eq2 = (-1 + t2 + (2 + 6*t1 + 4*t1^2)*λ - 4*t2 *λ)/((1 + t1)^2) == 0
eq3 = (-57 + 16*t2 - 16*t2^2 + t1^2 (31 + 32*t2) + t1*(-2 - 32 t1*t2 + 48*t2)/(8*(1 + t1)^2)) == 0
sol = Solve[{eq1, eq2, eq3}, {t1, t2, λ}]


N[sol]