Question

Giải phương trình.

a)\(\sqrt[3]{x+1}-1=x\)

b)\(\sqrt[3]{1-x}+\sqrt[3]{1+x}=2\)

c) \(\sqrt[3]{x}+\sqrt[3]{2x-3}=\sqrt[3]{12\left(x-1\right)}\)

Answer 1

Đặt ẩn phụ

Answer 2

\(a,\sqrt[3]{x+1}=x+1\)

\(\Leftrightarrow\left(x+1\right)=\left(x+1\right)^3\)

\(\Leftrightarrow\left(x+1\right)\left[\left(x+1\right)^2-1\right]=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+1+1\right)\left(x+1-1\right)=0\)

\(\Leftrightarrow x\left(x+1\right)\left(x+2\right)=0\)

\(\Leftrightarrow x=0\left(h\right)x=-1\left(h\right)x=-2\)

Answer 3

\(b,\sqrt[3]{1-x}+\sqrt[3]{1+x}=2\)

\(\Leftrightarrow1-x+1+x+3\sqrt[3]{\left(1-x\right)\left(1+x\right)}\left(\sqrt[3]{1-x}+\sqrt[3]{1+x}\right)=8\)

\(\Leftrightarrow3\sqrt[3]{1-x^2}.2=6\)

\(\Leftrightarrow\sqrt[3]{1-x^2}=1\)

\(\Leftrightarrow x^2=0\)

\(\Leftrightarrow x=0\)

Answer 4

bạn giải thích bước 2 của câu a được không ạ?