Question

Himpunan penyelesaian persamaan 2cos²x + cos x-1 =0, untuk 0°<x<180°


itu kurang dari sama dengan yah kak

Answer 1

Cos x = x

• 2cos^2 + cosx -1 = 0
• 2x^2 + x -1 = 0
• (x+1)(2x-1) = 0
• x = -1 | x = 1/2

#X = -1
• cos x = -1
• cos x = -cos0
• cos x = -cos(180-0)
• cos x = 180°

•> x = 180° + k.360° (k=0)
•> x = 180° #memenuhi

•> x = -180° + k.360 (k = 1)
•> x = 180° #Memenuhi

#X = 1/2
• cos x = 1/2
• cos x = cos 60°
• x = 60°

•> x = 60° + k.360 (k = 0)
•> x = 60° #memenuhi

•> x = -60° + k.360 (k=1)
•> x = 300° #tidak memenuhi

Hp {60° , 180°}

Answer 2

Misal cos x =a
2a² + a  - 1 = 0
(2a -1)(a + 1) = 0
a = 1/2 atau a = -1

cos x = 1/2 = cos 60 atau cos x = -1 = cos 180
x = 60 , 180