Question

\(\text{Cho }a=\sqrt{3+2x}+\sqrt{3-2x}\)

\(\text{Tính }B=\frac{\sqrt{2-\sqrt{9-4x^2}}}{x}\)

Answer 1

\(B=\frac{\sqrt{3-\sqrt{9-4x^2}}}{x}\) sẽ hợp lý hơn, chứ biểu thức B đúng như bạn ghi thì ko rút gọn được theo a

Answer 2

\(a^2=6+2\sqrt{9-4x^2}\Rightarrow\sqrt{9-4x^2}=\frac{a^2-6}{2}\)

\(\Rightarrow9-4x^2=\frac{\left(a^2-6\right)^2}{4}\Rightarrow x^2=\frac{36-\left(a^2-6\right)^2}{16}=\frac{a^2\left(12-a^2\right)}{16}\)

\(\Rightarrow B=\pm\sqrt{\frac{3-\sqrt{9-4x^2}}{x^2}}=\pm\sqrt{\frac{3-\frac{a^2-6}{2}}{x^2}}=\pm\sqrt{\frac{12-a^2}{2x^2}}\)

\(\Rightarrow B=\pm\sqrt{\frac{8\left(12-a^2\right)}{a^2\left(12-a\right)^2}}=\pm\sqrt{\frac{8}{a^2}}=\pm\frac{2\sqrt{2}}{a}\)