Question

if a² + 1/a² = 18 find rhe value of a + 1/a and a -. 1/a​

Answer 1

EXPLANATION.

⇒ (a² + 1/a²) = 18.

As we know that,

Formula of :

⇒ (x + y)² = x² + y² + 2xy.

We can write equation as,

⇒ (a + 1/a)² = a² + 1/a² + 2(a)(1/a).

⇒ (a + 1/a)² = a² + 1/a² + 2.

Put the values of (a² + 1/a²) = 18 in equation, we get.

⇒ (a + 1/a)² = 18 + 2.

⇒ (a + 1/a)² = 20.

⇒ (a + 1/a) = √20.

⇒ (a + 1/a) = 2√5.

As we know that,

Formula of :

⇒ (x - y)² = x² + y² - 2xy.

Using this formula in the equation, we get.

⇒ (a - 1/a)² = a² + 1/a² - 2(a)(1/a).

⇒ (a - 1/a)² = a² + 1/a² - 2.

Put the values of (a² + 1/a²) = 18 in equation, we get.

⇒ (a - 1/a)² = 18 - 2.

⇒ (a - 1/a)² = 16.

⇒ (a - 1/a) = √16.

⇒ (a - 1/a) = 4.