Question

|2x^2 + 7/16| - |1+x^2| = 0

Answer 1

|2x² + 7/16| - |1+x²| = 0

=>|2x²+7/16|=|1+x²|

=>2x²+7/16=1+x² hoặc >2x²+7/16==1-x²

=>2x²-x²=1-7/16 hoặc 2x²+x²=-1-7/16

x²=9/16 hoặc 3x²=-23/16(vô lí)

x=3/4 hoặc x=-3/4

Answer 2

Ta có: \(\left|2x^2+\frac{7}{16}\right|=\left|1+x^2\right|\)

\(\Rightarrow\orbr{\begin{cases}2x^2+\frac{7}{16}=1+x^2\\2x^2+\frac{7}{16}=-1-x^2\end{cases}\Rightarrow\orbr{\begin{cases}x^2=\frac{9}{16}\\3x^2=-\frac{23}{16}\left(vn\right)\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{3}{4}\\x=-\frac{3}{4}\end{cases}}}\)

                  Vậy x = 3/4 , x = -3/4