A Very Nice Math Olympiad Problem | What Is The Value Of x | You Need To Know This Trick | Algebra

[@skyrider53]

2:09 You ain’t slick my boy

[@에스피-z2g]

1/x=t
t^2-t^3=80
t^2(1-t)=80
(-4)^2(1+4)=80
t=-4
x=-1/4

[@SpencersAcademy]

Great job 👏

[@prollysine]

let 1/x=u , u^3-u^2+/-u+80=0 , (u+4)(u^2-5u+20)=0 , U= -4 , 1/x= -4 , x= -1/4 , 1/x=1/(-1/4) ,
1 4 test --> (1/x)^2=16 , -(1/x)^3= -(-64) , --> 64 , ergo , 16+64=80 , OK , solu , x= -1/4 ,
-5 -20
20 80

[@SpencersAcademy]

Awesome 👌

[@ShriH-d1o]

=> 80x³ - x +1= 0;
=> 64x³+1 +16x³ -x =0;
=> (4x+1)(16x²-4x+1)+
x(16x²-1)=0; =>(4x+1)
(16x²-4x+1)+x(4x-1)(4x+1);=>(4x+1)(16x²-4x+1+4x²-x);=>
(4x+1)(20x²-5x+1); =>
x= - 1/4 ✓ & x={5±√(25-80)}/40
x={5±i√55)}/40 ✓
]

[@SpencersAcademy]

Excellent job 👏