Odpowiedź:
[tex](x-1)^2-2(x-3)>(x+\sqrt{5})(x-\sqrt{5})\\\\x^2-2x+1-2x+6>x^2-(\sqrt{5})^2 \\\\x^2-4x+7>x^2-5\\\\x^2-4x-x^2>-5-7\\\\-4x>-12\ \ /:(-4)\\\\x<3\\\\x\in(-\infty,3)\\\\\\\\(10p+9)^2-(8p+7)^2>(6p+5)^2+5\\\\100p^2+180p+81-(64p^2+112p+49)>36p^2+60p+25+5\\\\100p^2+180p+81-64p^2-112p-49>36p^2+60p+30\\\\36p^2+68p+32>36p^2+60p+30\\\\36p^2+68p-36p^2-60p>30-32\\\\8p>-2\ \ /:8\\\\p>-\frac{2}{8}\\\\p>-\frac{1}{4}\\\\x\in(-\frac{1}{4},+\infty)[/tex]
Szczegółowe wyjaśnienie:
[tex]Zastosowane\ \ wzory\\\\(a-b)^2=a^2-2ab+b^2\\\\(a+b)=a^2+2ab+b^2\\\\(a-b)(a+b)=a^2-b^2[/tex]