If a 2 − 7 a + 1 = 0 and a = ≠ 0, Find : a + 1 a

If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :

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

Sum

Dividing the given equation by a, we get:

`"a"^2/"a" - (7"a")/"a" + 1/"a" = 0, "a" - 7 + 1/"a" = 0`

⇒ `"a" + (1)/"a"` = 7.

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Chapter 4: Expansions - Exercise 4.1

Chapter 4 Expansions
Exercise 4.1 | Q 15.1

Prove that a² + b² + c² − ab − bc − ca is always non-negative for all values of a, b and c

If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]

Evaluate of the following:

(99)³

(a − b)³ + (b − c)³ + (c − a)³ =

Use the direct method to evaluate the following products :
(b – 3) (b – 5)

Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`

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

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

If x + y = 1 and xy = -12; find:
x² - y².

Simplify:
(3a - 7b + 3)(3a - 7b + 5)