Question

The number of real solution of x-1/x^2-4=-2-1/x^2-4

Answer 1

$\sf{x-\dfrac{1}{x^2-4}=2-\dfrac{1}{x^2-4} }$

$\displaystyle{\sf{For\ a\ quadratic\ rquation,\ (x^2-4)\neq 0}}$

As, if it becomes equal to 0, then the value becomes infinity.

Solving it :-

$\displaystyle{\sf{\implies x^2-4\neq0}}\\\\\displaystyle{\sf{\implies x^2 \neq 4}}\\\\\displaystyle{\sf{\implies x \neq \sqrt{4}}}\\\\\displaystyle{\sf{\implies x\neq 2,\ -2 }}$

Now, solving the given quadratic equation :-

$\displaystyle{\sf{\hookrightarrow x-2=-\frac{1}{x^2-4}+\frac{1}{x^2-4} }}\\\\\displaystyle{\sf{\hookrightarrow x-2=0}}\\\\\displaystyle{\sf{\hookrightarrow x=2}}$

But, as proved earlier, x ≠ 2.

Hence, we conclude that, the given quadratic equation has no real solutions.

Answer 2

Answer:

sorry,I'm not able to understand the question.