Given the vector a = (cos3 / 2x, SIN3 / 2x), B = (cosx / 2, - SiNx / 2), and X belongs to [π / 2, π],. | a + B | is greater than the root sign 3, find the value range of X

Given the vector a = (cos3 / 2x, SIN3 / 2x), B = (cosx / 2, - SiNx / 2), and X belongs to [π / 2, π],. | a + B | is greater than the root sign 3, find the value range of X

a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),|a+b|>√3,∴(a+b)^2=(cos3/2x+cosx/2)^2+(sin3/2x-sinx/2)^2=2+2(cos3/2xcosx/2-sin3/2xsinx/2)=2+2cos2x>3,∴cos2x>1/2,x∈[π/2,π],∴2x∈[π,2π],∴5π/3