Math Olympiad| Many failed this math question|Algebra.

[@devonwilson5776]

Greetings. Absolutely intriguing. Blessings.

[@RyanLewis-Johnson-wq6xs]

X^5+X^4+X^3+X^2+X+1=0 X=-1 X=±0.5±0.5Sqrt[3]i=(±1±Sqrt[3]i)/2

[@key_board_x]

x⁵ + x⁴ + x³ + x² + x + 1 = 0
(x⁵ + x⁴ + x³) + (x² + x + 1) = 0
x³.(x² + x + 1) + (x² + x + 1) = 0
(x³ + 1).(x² + x + 1) = 0
(x³ + 1³).(x² + x + 1) = 0 → recall: a³ + b³ = (a + b).(a² - ab + b²) → x³ + 1³ = (x + 1).(x² - x + 1)
(x + 1).(x² - x + 1).(x² + x + 1) = 0
First case: (x + 1) = 0
→ x = - 1
Second case: (x² - x + 1) = 0
x² - x = - 1
x² - x + (1/4) = - 1 + (1/4)
[x - (1/2)]² = - 3/4
[x - (1/2)]² = 3i²/4
[x - (1/2)]² = [± (i√3)/2]²
x - (1/2) = ± (i√3)/2
x = (1/2) ± [(i√5)/2]
→ x = (1 ± i√3)/2
Third case: (x² + x + 1) = 0
x² + x = - 1
x² + x + (1/4) = - 1 + (1/4)
[x + (1/2)]² = - 3/4
[x + (1/2)]² = 3i²/4
[x + (1/2)]² = [± (i√3)/2]²
x + (1/2) = ± (i√3)/2
x = - (1/2) ± [(i√5)/2]
→ x = (- 1 ± i√3)/2

[@HenryEkhator-g9r]

Good

[@francisamewode233]

Perfect. Love your class very much.

[@JJONLINEMATHSCLASSchannel]

I appreciate

[@rajindersingh-jx1xl]

Talented JJ 🎉🎉🎉

[@JJONLINEMATHSCLASSchannel]

Thanks

[@RyanLewis-Johnson-wq6xs]

It’s in my head.

[@JJONLINEMATHSCLASSchannel]

👍👍

[@drashokkumar9209]

X = -- 1

[@JJONLINEMATHSCLASSchannel]

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