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 3: Expansions - Exercise 4.1

Chapter 3 Expansions
Exercise 4.1 | Q 15.1

Simplify (a + b + c)² + (a - b + c)²

If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`

Find the following product:

\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]

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

If a - b = 7 and ab = 18; find a + b.

Evaluate: (9 − y) (7 + y)

Find the squares of the following:
3p - 4q²

Simplify by using formula :

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

If m - n = 0.9 and mn = 0.36, find:
m² - n².

If a + b + c = 0, then a³ + b³ + c³ is equal to ______.