Question

If x2+1/x2=23,find x+1/x

Answer 1

EXPLANATION.

⇒ (x² + 1/x²) = 23.

As we know that,

Formula of :

⇒ (a + b)² = a² + b² + 2ab.

Using this formula in the equation, we get.

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

⇒ (x + 1/x)² = x² + 1/x² + 2.

Put the value of (x² + 1/x² = 23) in the equation, we get.

⇒ (x + 1/x)² = 23 + 2.

⇒ (x + 1/x)² = 25.

⇒ (x + 1/x) = √25.

⇒ (x + 1/x) = ± 5.

Answer 2

given

x² + 1/x² =23

Adding 2 in both sides

➡x² + 1/x² +2 = 23+2

➡x² + 1/x² + 2.x.1/x =25

➡(x + 1/x )²=25

➡x + 1/x = ± 5