a^2 + 1a^2 14 = a^2 + 1a^2 + 2 16 = (a + 1a)^2 (4)^2 = (a + 1a + 4) ( a + 1a 4 ) ∴ a^2 + 1a^2 14 = (a + 1a + 4) ( a + 1a 4 ...

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Factorisation of Quadratic Polynomials

Factorize a2...

Question

Factorize
$a^{2} + \frac{1}{a^{2}} - 14$

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Solution

$a^{2} + \frac{1}{a^{2}} - 14$

$= a^{2} + \frac{1}{a^{2}} + 2 - 16$

$= {(a + \frac{1}{a})}^{2} - (4)^{2}$

$= (a + \frac{1}{a} + 4) (a + \frac{1}{a} - 4)$

$∴ a^{2} + \frac{1}{a^{2}} - 14 = (a + \frac{1}{a} + 4) (a + \frac{1}{a} - 4)$

Hence factorized.

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