If "A"^2+ 1/"A"^2=23, Find : "A" +1/"A"

If `"a"^2+ 1/"a"^2=23`, find : `"a" +1/"a"`

Sum

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

`⇒("a"+1/"a")^2=23+2`

`⇒("a"+1/"a")^2=25`

`⇒"a"+1/"a"=sqrt25`

`⇒"a"+1/"a"=±5`

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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 7 | Page 154

If a² + b² = 29 and ab = 10, find : a + b

If a² + b²= 10 and ab = 3; find : a + b

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

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

Find : `"a"^3+1/"a"^3`, if `"a" +1/"a"=5`.

Find:

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

If `2"x"-1/(2"x")=4`, find: `8"x"^3-1/(8"x"^3)`

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

If 3x + 2y = 9 and xy = 3, find : 27x³ + 8y³.

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