## 355 Reputation

7 years, 243 days

## How to get coordinates of triangle ABC k...

Maple 2018

I want to find one option of coodiantes of vertices A, B, C of the triangle ABC, knowing that coordinates centre of circumcircle is O(0,0) and length of sides are 3, 5, 7.
How can I get the result?

## How to get the result of this limit?...

Maple 2018

How to get the result of this limit? I don't get the result.

`limit(sum(1/(i*sqrt(i+1)+(i+1)*sqrt(i)), i = 1 .. n), n = infinity);`

With Mathematica, I got the output is 1.

## Bugs with RealDomain:-solve ?...

Maple 2018

I want to solve the equation (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0 in RealDomain. I tried

```restart;
RealDomain:-solve({(-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0}, {x});```

I got four solutions

If I work around

```restart;
RealDomain:-solve({-x^2+4*x > 0, (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0}, x);```

I only got two solutions

With Mathematica, I got three solutions

That is mean, Maple lost the solution x = 5*Pi/4. I check this thing

f:= x-> (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(4*x-x^2) ;
f(5*Pi/4);

and got the result 0.

Are these bugs?

## How can I solve this trigonometric equat...

Maple 2018

The equation sin(9*x-(1/3)*Pi) = sin(7*x-(1/3)*Pi) can be solved easy by hand with solutions k*Pi and -Pi/48 + K*Pi/8. With Maple, I tried
solve({sin(9*x-(1/3)*Pi) = sin(7*x-(1/3)*Pi)}, x, explicit, allsolutions)

I don't get the above solutions. How can I get these solutions?

## How many solutions are there in the equa...

Maple 2018

Based on the equation at here https://www.mapleprimes.com/questions/209660-Problem-With-RealDomainsolve

I tried solve the equation (x-1)*sqrt(x^2 - 4)=0 in Real domain. My code
restart;
RealDomain:-solve((x-1)*sqrt(x^2-4) = 0, x);

I got there solutions are 1, 2, -2.  I think, If we solve the given in RealDomain, we only get two solutions -2 and 2.

My question is: How many solutions are there in the equation (x-1)*sqrt(x^2 - 4)=0 by RealDomain:-solve?

Two pictures by using Mathematica.

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