Question

Q1.If x2 +1/x2 =2 then x2-1/x2 = ?

Answer 1

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

Given,

$x^2+\frac{1}{x^2}=2$

We know that by using,

(a - b)² = a² + b² + 2ab

We have,

$\begin{gathered}(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2\times x\times\frac{1}{x}\\\;\\(x-\frac{1}{x})^2=2-2\\\;\\(x-\frac{1}{x})^2=0\\\;\\x-\frac{1}{x}=0\end{gathered}$

Now,

$(x^2-\frac{1}{x^2})=(x+\frac{1}{x})(x-\frac{1}{x})\;\;\;\;\;\;\;\;\;[\because a^2-b^2=(a+b)(a-b)]$

$\begin{gathered}(x^2-\frac{1}{x^2})=(x+\frac{1}{x})\times 0\\\;\\(x^2-\frac{1}{x^2})=0\end{gathered}$