A very nice Olympiad Math Cubic problem l find all possible solutions of x=?.

A very nice Olympiad Math Cubic problem l find all possible solutions of x=?.#maths #matholympics #mathproblem #matheolympiad #mathematics #mathcompetition #education #mathcontest #mathstricks #mathviral #mathviralvideo #mathviraltricks #cubicequation

[michaeldoerr]

I have never thought of that first step before. Looks like I will have to use that for further practice!!!

[sunnysharma]

X=±(1/2), but after verifying we will get x=-(1/2)only

[taniacsibi]

Soluțiile: x1= -1/2. X2, x3= _1\4 +, -5^1\2 \4

[HabibAkili]

x³ + x² = 1/8
Notice that 1/8=2/8 - 1/8= 1/4 - 1/8 = 1/2² - 1/2³
So
x³ + x² = 1/8
= 1/2² - 1/2³
Thus
x³+1/2³ + x²-1/2²=0
( x³+1/2³) + [ (x+1/2) (x-1/2)] = 0
[ (x+1/2) ( x²-(1/2)x+1/2²)]=x³+1)2³÷
(x+1/2) [ x-1/2+1/4-x/2+x²] =0
(x+1/2) (x²+x/2-1/4) =0
(x+1/2)=0
or
(x²+x/2-1/4)=0
∆=1/2²- 4×(1)×(-1/4)=5/4
√∆=√5/2
X'= (-1/2+√5/2)/2=√5-1/4
x'= -√5-1/4
and x= -1/2 are the solutions