Problem: If x= $\frac{4}{5}$, then = $\frac{\sqrt{1+x+\sqrt{1-x}}}{\sqrt{1+x-\sqrt{1-x}}}$?
View all: RAJSHAHI KRISHI UNNAYAN BANK OFFICER (SO) | WRITTEN QUESTION (MATH) SOLVE | 2014
Correct Answer: ans.2
Explanation:
দেওয়া আছে, x= $\frac{4}{5}$
=> $\frac{1}{x}$ =$\frac{4}{5}$
=>$\frac{1+x}{1-x}$= $\frac{5+4}{5-4}$ [যোজন বিয়োজন করে]
=>$\frac{1+x}{1-x}$= $\frac{9}{1}$
=> $\sqrt{\frac{1+x}{1-x}}$= $\sqrt{9}$ [বর্গমূল করে]
=> $\sqrt{\frac{1+x}{1-x}}$ =3
=>$\frac{\sqrt{1+x+\sqrt{1-x}}}{\sqrt{1+x-\sqrt{1-x}}}$=$\frac{3+1}{3-1}$ [আবার যোজন বিয়োজন করে]
=>$\frac{\sqrt{1+x+\sqrt{1-x}}}{\sqrt{1+x-\sqrt{1-x}}}$= $\frac{4}{2}$
=>$\frac{\sqrt{1+x+\sqrt{1-x}}}{\sqrt{1+x-\sqrt{1-x}}}$= 2
