1z. a+1/a=130/63 /*a a²+1/1=130a/63 63*(a²+1)=130a 63a²+63-130a=0 63a²-130a+63=0 Δ=(-130)²-4*63*63 Δ=16 900-15 876 Δ=1024 sqrtΔ=32 a1=130-32/126=0,777777778 a2=130+32/126=1,28571429
[latex]Zad.1.\ x+frac{1}{x}=frac{130}{63}\\ frac{x^2+1}{x}=frac{130}{63}\\ x^2+1=frac{130}{63}x\\ x^2-frac{130}{63}+1\\ Delta=(frac{130}{63})^2-4=frac{16900}{3969}-frac{15876}{3969}=frac{1024}{3969}\\ sqrtDelta=frac{32}{63}\\ x_1=frac{frac{130}{63}+frac{32}{63}}{2}=frac{frac{162}{63}}{2}=frac{frac{18}{7}}{2}=frac{18}{7}*frac{1}{2}=frac{9}{7}\\ x_2=frac{frac{130}{63}-frac{32}{63}}{2}=frac{frac{98}{63}}{2}=frac{frac{14}{9}}{2}=frac{14}{9}*frac{1}{2}=frac{7}{9}[/latex] [latex]Zad.2.\ frac{x+2}{2x^4-x^3} : frac{6x+4}{4x^3-x} = frac{6x+3}{x^3}\\ frac{x+2}{x^3(2x-1)}*frac{x(4x^2-1)}{6x+4}=frac{6x+3}{x^3}\\ frac{(x+2)(2x+1)}{x^2(6x+4)}=frac{3(2x+1)}{x^3}\\ frac{x+2}{6x+4}=frac{3}{x}\\ x(x+2)=3(6x+4)\\ x^2+2x-18x-12=0\\ x^2-16x-12=0\\ Delta=256+48=304\\ sqrtDelta=sqrt{304}=4sqrt{19}\\ x_1=frac{16+4sqrt{19}}{2}=8+2sqrt{19}\ x_2=frac{16-4sqrt{19}}{2}=8-2sqrt{19}[/latex]
