a)
[tex]16x^2+25=40x\\16x^2-40x+25=0\\(4x-5)^2=0\\4x-5=0\\4x=5\ |:4\\x=\frac{5}{4}\\x=1\frac{1}{4}[/tex]
b)
[tex]2x^2-6x=(2x-3)^2+(x+1)(x+2)\\2x^2-6x=4x^2-12x+9+x^2+2x+x+2\\2x^2-6x=5x^2-9x+11\\-3x^2+3x-11=0\\\Delta=3^2-4*(-3)*(-11)=9-132=-123 < 0[/tex]
równanie sprzeczne, brak rozwiązań
c)
[tex]3(x+5)(6-x) < 0\ |:3\\(x+5)(6-x) < 0\\x\in(-\infty,-5)\cup(6,+\infty)[/tex]
d)
[tex]9-(2x-1)^2\geq 0\\(3-2x+1)(3+2x-1)\geq 0\\(-2x+4)(2x+2)\geq 0\\-2(x-2)*2(x+1)\geq 0\\-4(x-2)(x+1)\geq 0\ |:(-4)\\(x-2)(x+1)\leq 0\\x\in < -1,2 >[/tex]
