Question

Rút gọn

a)\(\sqrt{2x-\sqrt{4x-1}}-\sqrt{2x+\sqrt{4x-1}}\) (với \(\dfrac{1}{4}\le x\le\dfrac{1}{2}\)

Answer 1

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

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

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

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

\(A^2=4x-2\sqrt{\left(2x-1\right)^2}\)

\(A^2=4x-2\left|2x-1\right|\)

\(A^2=4x-2\left(1-2x\right)\) (vì\(\dfrac{1}{4}\le x\le\dfrac{1}{2}\)

\(A^2=8x-2\)

\(A=\sqrt{8x-2}\)