factorize x²+1/x²-3
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ANSWER.
SOLUTION.
Given –
= x² + 1/x² - 3
We can write the expression as –
= x² + 1/x² - 2 - 1
Clearly, we observe that, x² + 1/x² - 2 is a perfect square. So, we get,
= (x - 1/x)² - (1)²
Now, factorise as difference of two squares, we get,
= (x - 1/x + 1)(x - 1/x - 1)
Which is our required answer.