|
|
dk $x$$\geq $2 hoặc $x$$\leq $-2
A=$\sqrt{\frac{x^{2}}{4}+\sqrt{x^{2}-4}}$+$\sqrt{\frac{x^{2}}{4}-\sqrt{x^{2}-4}}$=$\sqrt{\frac{x^{2}-4}{4}+\sqrt{x^{2}-4}+1}$+$\sqrt{\frac{x^{2}-4}{4}-\sqrt{x^{2}-4}+1}$
=$\sqrt{(\frac{\sqrt{x^{2}-4}}{2}+1)^{2}}$+$\sqrt{(\frac{\sqrt{x^{2}-4}}{2}-1)^{2}}$=$\left| {\frac{\sqrt{x^{2}-4}}{2}+1} \right|$+$\left| 1-{\frac{\sqrt{x^{2}-4}}{2}} \right|$$\geq$$\left| {\frac{\sqrt{x^{2}-4}}{2}+1+1-\frac{\sqrt{x^{2}-4}}{2}} \right|$=2
Vay MinA=2<=>$(\frac{\sqrt{x^{2}-4}}{2}+1)$$(1-\frac{\sqrt{x^{2}-4}}{2})$$\geq$0
<=>$-2\sqrt{2}$$\leq $$x$$\leq $$2\sqrt{2}$
Ket hop dk=>$2$$\leq $$x$$\leq $$2\sqrt{2}$ hoac $-2\sqrt{2}$$\leq$$x$$\leq$$2$
|