MathLabs

Problem 4

Find all real solutions of cos⁡2x+cos⁡22x+cos⁡23x=1\cos^2 x+\cos^2 2x+\cos^2 3x=1.
Step 3 of 5: Factor the resulting polynomial
16c6−20c4+6c2=0⟺2c2(4c2−3)(2c2−1)=016c^6-20c^4+6c^2=0\Longleftrightarrow2c^2(4c^2-3)(2c^2-1)=0
Detailed analysis

Expanding and moving 11 to the left gives 16c6−20c4+6c2=016c^6-20c^4+6c^2=0. Factoring yields 2c2(4c2−3)(2c2−1)=02c^2(4c^2-3)(2c^2-1)=0.