Question

Factorise x^2 +1/x^2-3​

Answer 1

Question :

Factorise :

$\sf x {}^{2} + \dfrac{1}{x {}^{2} } - 3$

Formula's used:

Algebra Identities

$\sf(x + y)(x - y) = x {}^{2} - y {}^{2}$

$\sf(x - y) {}^{2} = x {}^{2} + y {}^{2} - 2xy$

$\sf(x + y) {}^{2} = x {}^{2} + y {}^{2} + 2xy$

Solution :

We have to factorise

$\sf x {}^{2} + \dfrac{1}{x {}^{2} } - 3$

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

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

Now use formula (a-b)²=a²+b²-2ab

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

Now use formula a²-b² = (a+b)(a-b)

$\sf = (x - \dfrac{1}{x} - 1)(x - \dfrac{1}{x} + 1)$

It is the required solution!

Note :

Graph of $\sf x {}^{2} + \dfrac{1}{x {}^{2} } - 3$ in the attachment

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More About Factorization:

a factorization method called "grouping."

Answer 2

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$\huge\tt{GIVEN:}$

• x² +1/x²-³

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$\huge\tt{FACTORISING:}$

↪x² + 1/x² - 3

↪x²+1/x² - 2 - 1

↪x² + 1/x² - 2 * x * 1/x - 1

↪(x - 1/x)² - 1

↪(x - 1/x - 1) (x - 1/x + 1)

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