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If "A" + 1/"A"=3, Find "A"^2+1/"A"^2 - Mathematics

Sum

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`

Concept: Application of Formulae
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 12 Identities
Exercise 12 (C) | Q 5 | Page 154
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