Question

If x = (2 - √3), find the value of (x² + 1/x²).​

Answer 1

EXPLANATION.

⇒ x = (2 - √3).

As we know that,

We can write equation as,

⇒ 1/x = 1/(2 - √3).

Rationalizes the equation, we get.

⇒ 1/x = 1/(2 - √3) x (2 + √3)/(2 + √3).

⇒ 1/x = [(2 + √3)/(2 - √3)(2 + √3)].

⇒ 1/x = [(2 + √3)/(4 - 3)].

⇒ 1/x = 2 + √3.

To find value of : (x² + 1/x²).

As we know that,

Formula of :

⇒ (a + b)² = a² + b² + 2ab.

Put the values in this equation, we get.

⇒ (x + 1/x)² = (x)² + 1/(x)² + 2(x)(1/x).

⇒ (x + 1/x)² = x² + 1/x² + 2.

⇒ [(2 - √3) + (2 + √3)]² = x² + 1/x² + 2.

⇒ [2 - √3 + 2 + √3]² = x² + 1/x² + 2.

⇒ (4)² = x² + 1/x² + 2.

⇒ 16 = x² + 1/x² + 2.

⇒ x² + 1/x² = 14.

Value of (x² + 1/x²) = 14.