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[Huuduc921996]

Giải phương trình: $\sqrt{1-x^2}+\sqrt[4]{x^2+x-1}+\sqrt[6]{1-x}-1=0$

[Hoang Tung 126]

Sử dụng nhân liên hợp ta có :$\sqrt{(1-x)(1+x)}+\sqrt[6]{1-x}+(\sqrt[4]{x^2+x-1}-1)=0< = > \sqrt{(1-x)(1+x)}+\sqrt[6]{1-x}+\frac{(x-1)(x+2)}{(\sqrt[4]{x^2+x-1}+1)(\sqrt{x^2+x-1}-1)(\sqrt{x^2+x-1}+1)}=0< = > \sqrt[6]{1-x}(\sqrt{1+x}.\sqrt[6]{(1-x)^5}+\sqrt[3]{1-x}-\frac{\sqrt[6]{(1-x)^5}(x+2)}{(\sqrt[4]{x^2+x-1}-1)(\sqrt{x^2+x-1}-1)(\sqrt{x^2+x-1}+1)})=0= > x=1$