If P + 1 P = 6 ; Find : P 2 + 1 P 2 - Mathematics

If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`

Sum

`("p" + (1)/"p")^2`

= `"p"^2 + (1)/"p"^2 + 2`

⇒ 36 = `"p"^2 + (1)/"p"^2 + 2`

⇒ `"p"^2 + (1)/"p"^2`
= 36 - 2
= 34.

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Chapter 4: Expansions - Exercise 4.2

Chapter 4 Expansions
Exercise 4.2 | Q 10.1

Expand the following, using suitable identity:

(–2x + 3y + 2z)²

If a + b + c = 0 and a² + b² + c² = 16, find the value of ab + bc + ca.

If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`

If a + b = 6 and ab = 20, find the value of a³ − b³

If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]

If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

Expand the following:

`(2"a" + 1/(2"a"))^2`

Evaluate, using (a + b)(a - b)= a² - b².
4.9 x 5.1

Simplify:

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