To solve the equation 3cos^2(pix) + 4cos(pix) - 7 = 0, we can use a substitution to turn it into a quadratic equation in terms of cos(pi*x).
Let y = cos(pi*x), then the equation becomes:
3y^2 + 4y - 7 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula:
Using factoring: (3y - 1)(y + 7) = 0 y = 1/3 or y = -7
Now, remember that y = cos(pix), so we need to find the values of x for which cos(pix) is equal to 1/3 or -7. However, the cosine function only takes values between -1 and 1, so there are no solutions in this case.
Therefore, the equation 3cos^2(pix) + 4cos(pix) - 7 = 0 has no real solutions.
To solve the equation 3cos^2(pix) + 4cos(pix) - 7 = 0, we can use a substitution to turn it into a quadratic equation in terms of cos(pi*x).
Let y = cos(pi*x), then the equation becomes:
3y^2 + 4y - 7 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula:
Using factoring:
(3y - 1)(y + 7) = 0
y = 1/3 or y = -7
Now, remember that y = cos(pix), so we need to find the values of x for which cos(pix) is equal to 1/3 or -7. However, the cosine function only takes values between -1 and 1, so there are no solutions in this case.
Therefore, the equation 3cos^2(pix) + 4cos(pix) - 7 = 0 has no real solutions.