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 a+b=5 and ab = 6, find a² + b²

If a – b = 6 and ab = 16, find a² + b²

If a + b = 6 and ab = 8, find: a³ + b³.

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)`

The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.

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

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

The difference between the two numbers is 5 and their products are 14. Find the difference between their cubes.