Final answer:
To solve the equation 2cos²(x)+3cos(x)+1=0, we can let y = cos(x) and rewrite the equation as a quadratic equation. We can then solve the quadratic equation using the quadratic formula and find the values of y. Finally, we can find the corresponding values of x by taking the inverse cosine.
Step-by-step explanation:
To solve the equation 2cos²(x)+3cos(x)+1=0, we can let y = cos(x) and rewrite the equation as 2y²+3y+1=0. Now we can solve this quadratic equation for y using the quadratic formula. The quadratic formula is:
y = (-b ± √(b²-4ac)) / (2a)
Plugging in the values a=2, b=3, and c=1, we get y = (-3 ± √(3²-4(2)(1))) / (2(2)).
Simplifying this expression gives us two possible values for y. Once we have the values of y, we can find the corresponding values of x by taking the inverse cosine.