If a + 1 a = 6 ; Find a 2 − 1 a 2 - Mathematics

If `"a" + 1/"a" = 6;`find `"a"^2 - 1/"a"^2`

Sum

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

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

= (6)`(±4sqrt(2))`

= ±24`sqrt(2)`.

shaalaa.com

Is there an error in this question or solution?

Chapter 4: Expansions - Exercise 4.1

Chapter 4 Expansions
Exercise 4.1 | Q 9.2

Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`

Simplify the following expressions:

`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`

Evaluate of the following:

(103)³

Find the square of `(3a)/(2b) - (2b)/(3a)`.

Use identities to evaluate : (97)²

Simplify by using formula :
(2x + 3y) (2x - 3y)

Simplify by using formula :
(a + b - c) (a - b + c)

Evaluate the following without multiplying:
(1005)²

Simplify:
(x + 2y + 3z)(x² + 4y² + 9z² - 2xy - 6yz - 3zx)

Evaluate the following :
1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19