Question

\(G=\sqrt{2x+\sqrt{4x-1}-\sqrt{2x-\sqrt{4x-1}}}\)

Answer 1

\(G=\sqrt{2x+\sqrt{4x-1}-\sqrt{2x-\sqrt{4x-1}}}\) ; \(\left(x\ge\dfrac{1}{4}\right)\)

\(\Rightarrow\sqrt{2}.G=\sqrt{4x+2\sqrt{4x-1}-\sqrt{4x-2\sqrt{4x-1}}}\)

\(\Leftrightarrow\sqrt{2}.G=\sqrt{\left(\sqrt{4x-1}+1\right)^2-\left(\sqrt{4x-1}-1\right)^2}\)

\(\Leftrightarrow\sqrt{2}.G=\sqrt{\left(\sqrt{4x-1}+1-\sqrt{4x-1}+1\right)\left(\sqrt{4x-1}+1+\sqrt{4x-1}-1\right)}\)

\(\Leftrightarrow\sqrt{2}.G=\sqrt{2.\left(2\sqrt{4x-1}\right)}\)

\(\Leftrightarrow G=\sqrt{2\left(4x-1\right)}\)

 

Answer 2

Bạn xem lại xem đã viết biểu thức G đúng chưa vậy?