Question

GPT:

a)\(\frac{1}{2}-x^2=\sqrt{\frac{1}{2}-x}\)

b)\(\frac{x^2}{4}-2=\sqrt{4\left(x+2\right)}\)

Answer 1

a/ Đặt \(\sqrt{\frac{1}{2}-x}=a\)

b/ Đặt \(\sqrt{x+2}=a\)

Answer 2

a/ Đặt \(\sqrt{\frac{1}{2}-x}=a\)

\(\Rightarrow x=\frac{1}{2}-a^2\)

\(\Rightarrow\frac{1}{2}-\left(\frac{1}{2}-a^2\right)^2=a\)

\(\Leftrightarrow4a^4-4a^2+4a-1=0\)

\(\Leftrightarrow\left(2a^2-2a+1\right)\left(2a^2+2a-1\right)=0\)

Answer 3

b/ Đặt \(\sqrt{x+2}=a\)

\(\Rightarrow x=a^2-2\)

\(\Rightarrow\frac{\left(a^2-2\right)^2}{4}-2=2a\)

\(\Leftrightarrow a^4-4a^2-8a-4=0\)

\(\Leftrightarrow\left(a^2-2a-2\right)\left(a^2+2a+2\right)=0\)