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Question
If `"a" - 1/"a"=4`, find : `"a"^2+1/"a"^2`
Solution
`("a"-1/"a")^2="a"^2+1/"a"^2-2`
`⇒(4)^2="a"^2+1/"a"^2-2`
`⇒16="a"^2+1/"a"^2-2`
`⇒16+2="a"^2+1/"a"^2`
`⇒18="a"^2+1/"a"^2`
`∴"a"^2+1/"a"^2=18`
Alternative Method :
`"a" -1/"a"=4`
`⇒("a"-1/"a")^2=(4)^2`
`⇒"a"^2+1/"a"^2-2=16`
`⇒"a"^2+1/"a"^2=16+2`
`⇒"a"^2+1/"a"^2=18`
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