If a − 1 a = 10 ; Find a 2 − 1 a 2 - Mathematics

If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`

योग

`"a"^2 - 1/"a"^2`

= `("a" + 1/"a") ("a" - 1/"a")`

= `(±2sqrt(26)) (10)`
= ±20`sqrt(26)`.

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अध्याय 4: Expansions - Exercise 4.1

अध्याय 4 Expansions
Exercise 4.1 | Q 10.2

Factorise the following using appropriate identity:

9x² + 6xy + y²

Factorise:

`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`

Simplify the following products:

`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`

Write in the expand form: `(2x - y + z)^2`

Simplify the following expressions:

`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`

Evaluate the following:

(98)³

If \[x + \frac{1}{x} = 3\], calculate \[x^2 + \frac{1}{x^2}, x^3 + \frac{1}{x^3}\] and \[x^4 + \frac{1}{x^4}\]

If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]

Evaluate the following without multiplying:
(999)²

Evaluate the following without multiplying:
(1005)²