A Nice Cubic

🤩 Hello everyone, I'm very excited to bring you a new channel (SyberMath Shorts).
Enjoy...and thank you for your support!!! 🧡🥰🎉🥳🧡

If you need to post a picture of your solution or idea:
#algebra #polynomials #exponentials #logs #trigonometry #calculus
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva

PLAYLISTS 🎵 :

[walterwen]

A Nice Cubic: 4x³ – 10x² +14x – 5 = 0; x =?
2(4x³ – 10x² +14x – 5) = (2x)³ – 5(2x)² + 14(2x) – 10 = 0
Let: y = 2x; y³ – 5y² + 14y – 10 = 0, (y³ – 5y² + 4y) + (10y – 10) = 0
(y – 1)(y² – 4y) + 10(y – 1) = (y – 1)(y² – 4y + 10) = 0, y – 1 = 0 or y² – 4y + 10 = 0
y = 1 = 2x or y² – 4y + 4 = (y – 2)² = – 6 = (i√6)², y = 2x = 2 ± i√6
x =1/2 or x = (2 ± i√6)/2; Complex value roots
Answer check:
x = 1/2: 4x³ – 10x² +14x – 5 = 4/8 – 10/4 +14/2 – 5 = (1 – 5)/2 + 7 – 5 = 0; Confirmed
x = (2 ± i√6)/2: y = 2x, y² = 4y – 10; y³ = 4y² – 10y = 4(4y – 10) – 10y = 6y – 40
2(4x³ – 10x² +14x – 5) = y³ – 5y² + 14y – 10 = 0
y³ – 5y² + 14y – 10 = (6y – 40) – 5(4y – 10) + 14y – 10 = 0; Confirmed
Final answer:
x =1/2; Two complex value roots; x = (2 + i√6)/2 or x = (2 – i√6)/2

[prollysine]

by fakt., (2x-1)(2x^2-4x+5)=0, 2x-1=0, x=1/2, 2x^2-4x+5=0, x=1+iV3, 1-iV3,