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

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

योग

`("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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अध्याय 12: Identities - Exercise 12 (C) [पृष्ठ १५४]

अध्याय 12 Identities
Exercise 12 (C) | Q 8 | पृष्ठ १५४

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

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

If `"a" - 1/"a"=4`, 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 + b + c, if a² + b² + c² = 83 and ab + bc + ca = 71.

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

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

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