If "A"^2+ 1/"A"^2=11, Find : "A" -1/"A"

If `"a"^2+ 1/"a"^2=11`, find : `"a" -1/"a"`

Sum

`("a"-1/"a")^2="a"^2+1/"a"^2-2`

`⇒("a"-1/"a")^2=11-2`

`⇒("a"-1/"a")^2=9`

`⇒"a"-1/"a"=sqrt9`

`⇒"a"-1/"a"=±3`

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Application of Formulae

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Chapter 12: Identities - Exercise 12 (C) [Page 154]

Chapter 12 Identities
Exercise 12 (C) | Q 8 | Page 154

If `"a" + 1/"a"=3`, find `"a"^2+1/"a"^2`

If a + b + c = 10 and a² + b² + c² = 38, find : ab + bc + ca

Find: a² + b² + c², if a + b + c = 9 and ab + bc + ca = 24

Find:

`a^3-1/a^3`, if `a -1/a = 4`.

If `3"x"+1/(3"x")=3`, find : `9"x"^2+1/(9"x"^2)`

If `3"x"+1/(3"x")=3`, find : `27"x"^3+1/(27"x"^3)`

If a + b + c = 11 and a² + b² + c² = 81, find : ab + bc + ca.

If 3x – 4y = 5 and xy = 3, find : 27x³ – 64y³.

If a + b = 8 and ab = 15, find a³ + b³.

If 5x – 4y = 7 and xy = 8, find : 125x³ – 64y³.