If a − 1 a = 10 ; Find a 2 − 1 a 2

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 3: Expansions - Exercise 4.1

अध्याय 3 Expansions
Exercise 4.1 | Q 10.2

Verify:

x³ + y³ = (x + y) (x² – xy + y²)

Simplify the following:

322 x 322 - 2 x 322 x 22 + 22 x 22

Evaluate of the following:

(598)³

If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]

If a¹^/3 + b¹^/3 + c¹^/3 = 0, then

Evaluate: `(3"x"+1/2)(2"x"+1/3)`

Expand the following:
(2x - 5) (2x + 5) (2x- 3)

Simplify:
(7a +5b)² - (7a - 5b)²

Find the value of x³ + y³ – 12xy + 64, when x + y = – 4

If a + b + c = 5 and ab + bc + ca = 10, then prove that a³ + b³ + c³ – 3abc = – 25.