[tex]\textbf{\underline{\text{3.125}}}\\4x^4+9=37x^2\\4x^4-37x^2+9=0\\4x^4-36x^2-x^2+9=0\\4x^2(x^2-9)-1(x^2-9)=0\\(4x^2-1)(x^2-9)=0\\4(x^2-{1\over4})(x^2-9)=0\\(x^2-{1\over4})(x^2-9)=0\\(x-{1\over2})(x+{1\over2})(x-3)(x+3)=0\\x-{1\over2}=0\quad\vee\quad x+{1\over2}=0\quad\vee\quad x-3=0\quad\vee\quad x+3=0\\x={1\over2}\quad\vee\quad x=-{1\over2}\quad\vee\quad x=3\quad\vee\quad x=-3\\\boxed{x=\{-3,\,-{1\over2},\,{1\over2},\,3\}}\\\\[/tex]
[tex]\textbf{\underline{\text{3.126}}}\\x^4-25x^2=0\\x^2(x^2-9)=0\\x^2(x-3)(x+3)=0\\x^2=0\quad\vee\quad x-3=0\quad\vee\quad x+3=0\\x=0\quad\vee\quad x=3\quad\vee\quad x=-3\\\boxed{x=\{-3,\,0,\,3\}}[/tex]
[tex]\textbf{\underline{\text{3.131}}}\\x^2+4 > x\\x^2-x+4 > 0\\x^2-x+{1\over4}+3{3\over4} > 0\\x^2-2\cdot{1\over2}\cdot x+({1\over4})^2+3{3\over4} > 0\\(x-{1\over2})^2+3{3\over4} > 0\\(x-{1\over2})^2 > -3{3\over4}\\\\\text{Dowolne wyra\.zenie podniesione do kwadratu jest nieujemne, dlatego }(x-{1\over2})^2\\\text{bedzie zawsze wieksze od} -3{3\over4}.\\\\\boxed{x\in \mathbb{R}}[/tex]
[tex]\textbf{\underline{\text{3.134}}}\\(2x-1)^2 > 16\\(2x-1)^2-16 > 0\\(2x-1)^2-4^2 > 0\\(2x-1-4)(2x-1+4) > 0\\(2x-5)(2x+3) > 0\\4(x-2.5)(x+1.5) > 0\\(x-2.5)(x+1.5) > 0\\x-2.5 > 0\quad\vee\quad x+1.5 < 0\\x > 2.5\quad\vee\quad x < -1.5\\ \boxed{x\in(-\infty,\,-1.5)\cup(2.5,\,\infty)}[/tex]
[tex]\textbf{\underline{\text{3.112}}}\\(x-13)^2+1 = 0\\(x-13)^2 = -1\\\\\text{Dowolne wyra\.zenie podniesione do kwadratu jest nieujemne, dlatego }(x-13)^2\\\text{nigdy nie bedzie r\'owne} -1.\\\\\boxed{x\in \varnothing}[/tex]
[tex]\textbf{\underline{\text{3.113}}}\\16x^2+25=40x\\16x^2-40x+25=0\\(4x)^2-2\cdot4x\cdot5+5^2=0\\(4x-5)^2=0\\16(x-1{1\over4})^2=0\\(x-1{1\over4})^2=0\\x-1{1\over4}=0\\\boxed{x=1{1\over4}}[/tex]
