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Question
Factorise the following:
`"a"^2 + 1/"a"^2 - 18`
Sum
Solution
`"a"^2 + 1/"a"^2 - 18 = "a"^2 + 1/"a"^2 - 2 + 2 - 18`
...(add − 2 and + 2 to make 18 as 16)
= `"a"^2 + 1/"a"^2 - 2 xx "a" xx 1/"a" - 16` ...[a2 + b2 – 2ab = (a − b)(a − b)2]
= `("a" - 1/"a")^2 - 4^2` ...[a2 + b2 = (a + b)(a − b)]
= `("a" - 1/"a" + 4)("a" - 1/"a" - 4)`
shaalaa.com
Factorisation Using Identity a2 - b2 = (a + b)(a - b)
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