Răspuns:
[tex](\sqrt[3]{x}+\sqrt[3]{x-1})^{3}=1^{3},~(\sqrt[3]{x})^{3}+3*(\sqrt[3]{x})^{2}*\sqrt[3]{x-1}+3*\sqrt[3]{x}*(\sqrt[3]{x-1} ) ^{2}+(\sqrt[3]{x-1})^{3}= 1,~x+x-1+3*\sqrt[3]{x}*\sqrt[3]{x-1}*(\sqrt[3]{x} +\sqrt[3]{x-1})=1.~-1+3\sqrt[3]{x(x-1)}*1=1,~3\sqrt[3]{x(x-1)}=2~|^3,~27x(x-1)=8,~27x^{2}-27x-8=0[/tex]
Explicație pas cu pas:
Sper mai departe te ispravesti... calculezi Δ si x1 si x2, nu prea simpatici...
Δ=(-27)²-4·27·(-8)=27·(27+32)=27·59=9·3·59=9·177, deci √Δ=3√177
x1=(27-3√177)/(2·27)=(9-√177)/18 si x2=(9+√177)/18 .
