POMOCY!!!!! DAJE NAJ!!!!! Zadania znajdują się w załączniku.

[latex]zad.1)\\x^2-7x<0\\a>0 ramiona paraboli skierowane w gore\miejsca zerowe \ x(x-7)=0 \x=0 wedge x-7 =0\ x=0 wedge x=7 \ \ xin (0,7)[/latex] [latex](x+2)^2-1leq 2(x-3)^2\\x^2+4x+4-1leq 2(x^2-6x+9)\\x^2+4x+4-1leq 2 x^2-12x+18\\x^2+4x+4-1 -2 x^2+12x-18leq 0\\-x^2+16x-15leq 0 [/latex] [latex] Delta =b^2-4ac =16^2 -4* (-1)* (- 15)=256-60=196\ \sqrt{Delta }=sqrt{196}=14 \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{-16-14}{2 * (-1)}=frac{-30}{-2}=15\\x_{2}=frac{-b+ sqrt{Delta } }{2a}=frac{-16+14}{2 * (-1)}=frac{-2}{-2}=1 \ \xin(-infty ,1>cup <15,+infty )[/latex] [latex] zad.2)\\frac{2}{3+sqrt{5}}=frac{2}{3+sqrt{5}}*frac{3-sqrt{5}}{3-sqrt{5}}=frac{2(3-sqrt{5})}{9-5}=frac{2(3-sqrt{5})}{4}=frac{ 3-sqrt{5} }{2} [/latex] [latex] zad.3a)\\ (3x+y)^2=(3x)^2+2*3xy+y^2=9x^2+6xy+y^2\\\b)\\(sqrt{10}-sqrt{2})^2=(sqrt{10})^2+2*sqrt{10}*sqrt{2}+(sqrt{2}^2)=\\=10+2sqrt{20}+2=12+2sqrt{4*5}=12+2*2sqrt{5}=12+4sqrt{5}[/latex] [latex] zad.4)\\ frac{4}{9}a^2-b^2 =(frac{2}{9}a-b)(frac{2}{9}a+b)[/latex]