I am not sure why I am getting this RootOf result when I solve for x.

Here is my code.

restart:
eq:=4*x^2+2*y(x)^2=32.5625:
deq:=solve(  diff(eq,x), diff(y(x),x) ):
deq=3;
y(x)=solve(deq=3,y(x));
x=solve(deq=3,x);

The last equation we are solving is  -2x / y = 3.
So we should get y  = -2/3 x and  x = -3/2 y.

The Maple software correctly solves for y in terms of x,
but gives an odd Rootof answer when solving for x. Why is that?

I am not sure how to intepret RootOf(2*_Z+3*y(_Z)).

Hi. I wrote a command for finding second derivative.

#secondderiv test of f(x,y)
f:=x^2+2*x*y+2*y^3:
Gradient(f,[x,y]);
soln:=solve(Equate(Gradient(f,[x,y]),<0,0>));
H:=hessian(f,[x,y]);
seq([subs(soln[k],eval(H)),det(subs(soln[k],eval(H)))],k=1..nops(op(soln)))

Everything runs fine ... except if I change the function f to
f:=x^2+2*x*y+2*y^2
Then I get error :
Error, invalid input: nops expects 1 argument, but received 2

I sort of understand the error, when there is a single solution
{x=0,y=0} , then the op removes the parentheses to get x=0, y=0
which is now two arguments, and nops requires one argument.
I tried to use  nops(op({soln} ) , but that is not the correct approach
since it overcounts. Also it throws an error if change back f to the original expression.

I entered this function
f:=x->(4*x^2-4)^(4/5);

Then I entered f(0) and got (-4)^(4/5).

When I tried to approximate , I got -2.452480922+1.781831689*I

I am looking for the real number value, which is 3.031433 with my TI-83 calculator and here https://www.desmos.com/calculator/b1soxuhbri

How do I set it in maple so that x is assumed to be real in f(x) and all outputs are real.

I am trying to solve a factorial inequality.

solve(1/(n+1)! * exp(0.1)<=0.00001)

I get no result and a warning, "some solutions may have been lost".

Also same problem with the simpler inequality

solve(1/(n+1)! <=0.00001)

Wolfram has no problem solving it.

Am I entering it wrong? I attached a copy of my worksheet.

factorialinequality.mw

The problem came up when solving this problem: What degree of the maclaurin polynomial  is required so that the error in the approximation of e^0.1 is less than 0.00001

I am trying to solve the equation

exp(2*sin(t))-1=0, over the interval 0 <= t <=  16

I tried entering this into Maple:

solve({exp(2*sin(t))-1=0, 0 <= t,t <= 16}, AllSolutions, Explicit)

When I enter it, Maple just says "Evaluating"... and then returns nothing.

I tried "solve" without AllSolutions/Explicit, and even fsolve.

Then Maple only gives me the trivial result t = 0.

Is there a way to approximate the roots, like a root solver.

Ideally I would like to get the exact roots over the interval [0,16].

Wolfram has no problem solving this exactly.https://www.wolframalpha.com/input/?i=solve(%5Bexp(2*sin(t))-1%3D0,+0+%3C%3D+t,t+%3C%3D+16%5D,+AllSolutions,+Explicit)

I posted the worksheet

solveroots.mw