/!\ TESTED on HP-PRIME VIRTUAL CALCULATOR (Is Not an Emulator)

[CAS MODE & EXACT MODE ON & HP-PRIME "EMULATOR"]

solve( x^3+x=x,x); [ENTER] =>

{((-(v¬(5))-1)/2),0,((v¬(5)-1)/2)} // OK

[CAS & EXACT MODE OFF] (APPROXIMATE)

solve( x^3+x²=x,x); [ENTER] => { -1.61803398875, 0, 0.61803398875} // OK

decoding the previous output

x=-1.61803398875 OR x=0 OR x= 0.61803398875

x^3+x²=x|x=-1.61803398875; [ENTER] =>

-1.61803398875 = -1.61803398875

EVAL(Ans); [ENTER] => 1 (TRUE)

x^3+x²=x|x=0; [ENTER] =>

0 = 0

EVAL(Ans); [ENTER] => 1 (TRUE)

but

eq0:= x^3+x=x;

solve(eq0, x); [ENTER] => returns a different answer every time you press enter

[enter] => ...

**Another BUG with equations**

solve( x²-10*x+y² = -8 AND x*y²+x-10*y = -8 , { x ,y } ); [ENTER]

=> { [ 1, 1 ], [ 2.19343941541,3.02046646812 ] }

decoding the previous output

x = 1 and y = 1 or x = 2.19343941541 and y = 3.02046646812

[CAS MODE & EXACT MODE ON]

purge(x,y);

x²-10*x+y² = -8 AND x*y²+x-10*y = -8; => 0 ????? BUG

x²-10*x+y² = -8 AND x*y²+x-10*y = -8 | x = 1,y = 1; ==> 1 (true)

Left part (step to step):

x²-10*x+y² = -8|x= 1; => y²-9 = -8

y²-9 = -8|y = 1; =>

-8 = -8 => true

Right part:

x*y²+x-10*y = -8 |x= 1; => y²-10*y+1 = -8

y²-10*y+1 = -8|y = 1; =>

-8 = -8 => true

true and true => true

but

x²-10*x+y² = -8 AND x*y²+x-10*y = -8 | x = 1; => 0 ???? BUG

=> OK => y²-9 = -8 AND y²-10*y+1 => y²-9 = -8 AND y²-10*y+1

Ans| y=1 => true

[CAS & EXACT MODE OFF] (APPROXIMATE)

purge(x,y);

x²-10*x+y² = -8 AND x*y²+x-10*y = -8; => x²-10*x+y² = -8 AND x*y²+x-10*y = -8; // OK

x²-10*x+y² = -8 AND x*y²+x-10*y = -8 | x = 1,y = 1 ==> 1 (true)

x:=1;

y:=1;

x²-10*x+y² = -8 AND x*y²+x-10*y = -8 => 1 (true)

*Edited: 13 Oct 2013, 5:10 p.m. *