If 3"X"+1/(3"X")=3, Find : 9"X"^2+1/(9"X"^2)

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

Sum

`3"x"+1/"3x"=3`

`⇒(3"x"+1/"3x")^2=(3)^2`

`⇒(3"x")^2+(1/"3x")^2+2xx3"x"xx1/"3x"=9`

`⇒9"x"^2+1/"9x"^2+2=9`

`⇒9"x"^2+1/"9x"^2=9-2`

`⇒9"x"^2+1/"9x"^2=7`

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Chapter 12: Identities - Exercise 12 (C) [Page 155]

Chapter 12 Identities
Exercise 12 (C) | Q 17.1 | Page 155

If a+b=5 and ab = 6, find a² + b²

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

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)`

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.

If a + b + c = 9 and ab + bc + ca = 15, find: a² + b² + c².

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

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