![image](https://tex.z-dn.net/?f=%7C4x%5E2-12x%2B5%7C%285x%5E2-12x%2B4%29+%5Cgeq+0%2C+%5C%5C+%7C4x%5E2-12x%2B5%7C+%5Cgeq+0%5C+%5Cforall+x%5Cin+R%2C+%5C%5C+4x%5E2-12x%2B5%3D0%2C+%5C%5C+%5Cfrac%7BD%7D%7B4%7D+%3D16%2C+%5C%5C+x_1%3D+%5Cfrac%7B1%7D%7B2%7D%3D0%2C5+%2C+%5C+x_2%3D+%5Cfrac%7B5%7D%7B2%7D%3D2%2C5%3B+%5C%5C+5x%5E2-12x%2B4+%5Cgeq+0%2C+%5C%5C+5x%5E2-12x%2B4+%3D+0%2C+%5C%5C+%5Cfrac%7BD%7D%7B4%7D+%3D16%2C+%5C%5C+x_1%3D+%5Cfrac%7B2%7D%7B5%7D%3D0%2C4+%2C+%5C+x_2%3D2%3B+%5C%5C+D%3E0%2C+a%3E0%2C+%5C%5C+x%5Cin%28-%5Cinfty%3B0%2C4%5D%5Ccup%5B2%3B%2B%5Cinfty%29%5Ccup%5C%7B0%2C5%5C%7D)
0, a>0, \\ x\in(-\infty;0,4]\cup[2;+\infty)\cup\{0,5\}" alt="|4x^2-12x+5|(5x^2-12x+4) \geq 0, \\ |4x^2-12x+5| \geq 0\ \forall x\in R, \\ 4x^2-12x+5=0, \\ \frac{D}{4} =16, \\ x_1= \frac{1}{2}=0,5 , \ x_2= \frac{5}{2}=2,5; \\ 5x^2-12x+4 \geq 0, \\ 5x^2-12x+4 = 0, \\ \frac{D}{4} =16, \\ x_1= \frac{2}{5}=0,4 , \ x_2=2; \\ D>0, a>0, \\ x\in(-\infty;0,4]\cup[2;+\infty)\cup\{0,5\}" align="absmiddle" class="latex-formula">