Question

tìm x biết\(x^4+\sqrt{x^2+2012}=2012\)

Answer 1

\(x^4+\sqrt{x^2+2012}=2012.\)

\(\Leftrightarrow x^4=-\sqrt{x^2+2012}+2012.\)

\(\Leftrightarrow x^4+x^2+\frac{1}{4}=x^2+2012-\sqrt{x^2+2012}+\frac{1}{4}.\)

\(\Leftrightarrow\left(x^2+\frac{1}{2}\right)^2=\left(\sqrt{x^2+2012}-\frac{1}{2}\right)^2.\)

Đến đây chia 2 TH ra là ok

Answer 2

thank nhé

Answer 3

\(\Leftrightarrow\left(x^2+\frac{1}{2}\right)^2-\left(\sqrt{x^2+2012}-\frac{1}{2}\right)^2=0..\)

HĐT nha hoặc khai phương cx đc