Odpowiedź:
[tex]a)\\\\2(x+3)^2-(x-1)(x+1)=x^2\\\\2(x^2+6x+9)-(x^2-1)=x^2\\\\2x^2+12x+18-x^2+1=x^2\\\\x^2+12x+19=x^2\\\\x^2+12x-x^2=-19\\\\12x=-19\ \ /:12\\\\x=-\frac{19}{12}\\\\x=-1\frac{7}{12}\\\\\\b)\\\\5x^2-(x-3)^2\leq(2x-1)(2x+1)\\\\5x^2-(x^2-6x+9)\leq 4x^2-1\\\\5x^2-x^2+6x-9\leq 4x^2-1\\\\4x^2+6x-4x^2\leq -1+9\\\\6x\leq 8\ \ /:6\\\\x\leq \frac{8}{6}\\\\x\leq 1\frac{2}{6}\\\\x\leq 1\frac{1}{3}[/tex]
[tex]c)\\\\(2x+5)^2 > 4(x-3)(x+3)\\\\4x^2+20x+25 > 4(x^2-9)\\\\4x^2+20x+25 > 4x^2-36\\\\4x^2+20x-4x^2 > -36-25\\\\20x > -61\ \ /:20\\\\x > -\frac{61}{20}\\\\x > -3\frac{1}{20}\\\\\\Wykorzystane\ \ wzory\\\\(a+b)^2=a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2\\\\((a-b)(a+b)=a^2-b^2[/tex]
