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 a² + b²= 10 and ab = 3; find : a – b

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

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

Find : a + b + c, if a² + b² + c² = 83 and ab + bc + ca = 71.

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

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 = 8 and ab = 15, find a³ + b³.

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

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