b)
[tex]3x-(1-x)^2\geq (x-2)(x+2)\\3x-(1-2x+x^2)\geq x^2-2^2\\3x-1+2x-x^2\geq x^2-4|-x^2\\-2x^2+5x-1\geq -4|+4\\-2x^2+5x+3\geq 0\\\Delta=b^2-4ac\\\Delta=5^2-4*(-2)*3=25+24=49\\\sqrt{\Delta}=\sqrt{49}=7\\x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-5-7}{2*(-2)}=\frac{-12}{-4}=3\\x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-5+7}{2*(-2)}=\frac{2}{-4}=-\frac12[/tex]
x ∈ (-∞;-½> ∪ <3; ∞)
c)
[tex](x-3)^2-7\leq (2x-1)^2\\x^2-6x+9-7\leq4x^2-4x+1|-4x^2+4x-1\\-3x^2-2x+1\leq0\\\Delta=b^2-4ac\\\Delta=(-2)^2-4*(-3)*1=4+14=16\\\sqrt{\Delta}=\sqrt{16}=4\\x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*(-3)}=\frac{2-4}{-6}=\frac{-2}{-6}=\frac13\\x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*(-3)}=\frac{2+4}{-6}=\frac{6}{-6}=-1[/tex]
x ∈ <-1; ⅓>
