If 2"X"-1/(2"X")=4, Find : 4"X"^2+1/(4"X"^2) - Mathematics

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

Sum

`2"x"-1/"2x"=4`

`⇒(2"x"-1/"2x")^2=(4)^2`

`⇒(2"x")^2+(1/"2x")^2-2xx2"x"xx1/"2x"=16`

`⇒4"x"^2+1/"4x"^2-2=16`

`⇒4"x"^2+1/"4x"^2=16+2`

`⇒4"x"^2+1/"4x"^2=18`

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Application of Formulae

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

Chapter 12 Identities
Exercise 12 (C) | Q 16.1 | Page 155

If a+b=5 and ab = 6, find a² + b²

If `"a" - 1/"a"=4`, 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.

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

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 a² + b² = 41 and ab = 4, find : a – b

If 3x – 4y = 5 and xy = 3, find : 27x³ – 64y³.

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