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If "A" - 1/"A"=4, Find : "A"^2+1/"A"^2 - Mathematics

Sum

If `"a"  - 1/"a"=4`, find : `"a"^2+1/"a"^2`

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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`

Concept: Application of Formulae
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 12 Identities
Exercise 12 (C) | Q 6 | Page 154
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