Rozwiąż równanie: [latex]( sqrt[3]{4sqrt[4]{4} } )^{6x+6} = 8^{ frac{1}{3}x^2+3} [/latex]

[latex]left(sqrt[3]{4sqrt[4]{4} } ight) ^{6x+6} = 8^{ frac{1}{3}x^2+3}[/latex] dziedzina: [latex]x in R[/latex] [latex](left(sqrt[3]{2^2sqrt[4]{2^2} } ight) ^{6x+6} = (2^3)^{ frac{1}{3}x^2+3}[/latex] [latex]left( sqrt[3]{2^2 cdot (2^2)^{ frac{1}{4} } } ight) ^{6x+6} = 2^{x^2+9}[/latex] [latex]left( sqrt[3]{2^2 cdot 2^{ frac{1}{2} } } ight) ^{6x+6} = 2^{x^2+9}[/latex] [latex]left( sqrt[3]{2^{ frac{5}{2} } } ight) ^{6x+6} = 2^{x^2+9}[/latex] [latex]left((2^{ frac{5}{2} } })^{ frac{1}{3} } ight) ^{6x+6} = 2^{x^2+9}[/latex] [latex]left(2^{ frac{5}{6} } ight) ^{6(x+1)} = 2^{x^2+9}[/latex] [latex]2^{5(x+1)} = 2^{x^2+9}[/latex] [latex]5(x+1)=x^2+9[/latex] [latex]x^2+9=5x+5[/latex] [latex]x^2+9-5x-5=0[/latex] [latex]x^2-5x+4=0[/latex] [latex]Delta=(-5)^2-4 cdot 1 cdot 4=25-16=9[/latex] [latex]sqrt{Delta} = sqrt{9} =3[/latex] [latex]x_1= frac{5-3}{2}= frac{2}{2}=1[/latex] [latex]x_2= frac{5+3}{2}= frac{8}{2}=4[/latex]

1. Oblicz [latex]frac{4sqrt{2}}{sqrt{5}-1} - frac{2+sqrt{2}}{sqrt{2}+1}[/latex] 2. Rozwiąż równanie [latex]frac{(x-1)^{2}}{4} - frac{(x-2)^{2}}{6}= frac{x+1}{12} [/latex]

1. Oblicz [latex]frac{4sqrt{2}}{sqrt{5}-1} - frac{2+sqrt{2}}{sqrt{2}+1}[/latex] 2. Rozwiąż równanie [latex]frac{(x-1)^{2}}{4} - frac{(x-2)^{2}}{6}= frac{x+1}{12} [/latex]...