4cos2A = 3cosA for
cos 2A = 2cos^2 A -1
4(2 cos^2 A -1) = 3 cos A
8 cos^2 A - 4 - 3 cos A = 0
8 cos^2 A - 3 cos A - 4 = 0
Let cos A = x
8x^2-3x-4=0
This equation is of form ax^2+bx+c
a = 8 b = -3 c = -4
x=[-b+/-sqrt(b^2-4ac)]/2a]
x=[3 +/-sqrt(-3^2-4(8)(-4)]/(2)(8)
discriminant is b^2-4ac =137
x=[3 +√(137)] / (2)(8)
x=[3 -√(137)] / (2)(8)
x=[3+11.704699910719625] / 16
x=[3-11.704699910719625] / 16
The roots are 0.919 and -0.544
cos A = 0.919
SInce 90º≤A≤180º , A is in quadrant 2, where cos is negative.
Therefore, cos A = 0.919 has no solution.
cos A = -0.544
A= 2.146 (use a calculator and find the inverse of cos(-0.544).
A = 2.146 radians = 122.96 degrees
