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Question
If `"a" + 1/"a"=3`, find `"a"^2+1/"a"^2`
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Solution
`("a"+1/"a")^2="a"^2+1/"a"^2+2`
`⇒(3)^2="a"^2+1/"a"^2+2`
`⇒9="a"^2+1/"a"^2+2`
`⇒9-2="a"^2+1/"a"^2`
`⇒7="a"^2+1/"a"^2`
`∴"a"^2+1/"a"^2=7`
Alternative Method :
`"a" +1/"a"=3`
`⇒("a"+1/"a")^2=(3)^2`
`⇒"a"^2+1/"a"^2+2=9`
`⇒"a"^2+1/"a"^2=9-2`
`⇒"a"^2+1/"a"^2=7`
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