Question

Statement-1: The number of ordered pairs $(x,y)$ satisfying the equation $x^2+\frac{1}{x^2}=2^{1-y^2}$ is 2
Statement-2: The range of $x^2+\frac{1}{x^2}$ is $[2,\infty )$ and the range of $2^{1-y^2}$ is $(0,2]$.

• A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
• B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
• C. Statement-1 is true, statement-2 is false.
• D. Statement-1 is false, statement-2 is true. . .

Answer 1

Answer: (A)

We have $x^2+\frac{1}{x^2}=2^{1-y^2}=2$
$\therefore x=\pm 1$ and $y^2=0\Rightarrow y=0$.
Hence number of ordered pairs $(x,y)$ satisfying the equation will be 2 i.e. $(1,0)$ and $(-1,0)$.