If x⁴+1/x⁴ =119, find x²+1/x² and x +1/xPlease answer the questi

1.	If x⁴+1/x⁴ =119, find x²+1/x² and x +1/xPlease answer the question with explanation
Answer» EXPLANATION. ⇒ If x⁴ + 1/x⁴ = 119. As we know that, ⇒ (x² + 1/x²)² = x⁴ + 1/x⁴ + 2(x²)(1/x²). ⇒ (x² + 1/x²)² = x⁴ + 1/x⁴ + 2. Put the value of (x⁴ + 1/x⁴) = 119 in EQUATION, we get. ⇒ (x² + 1/x²)² = 119 + 2. ⇒ (x² + 1/x²)² = 121. ⇒ (x² + 1/x²) = √121. ⇒ (x² + 1/x²) = 11. As we know that, ⇒ (X + 1/x)² = x² + 1/x² + 2(x)(1/x). ⇒ (x + 1/x)² = x² + 1/x² + 2. Put the value of (x² + 1/x²) = 11 in equation, we get. ⇒ (x + 1/x)² = 11 + 2. ⇒ (x + 1/x)² = 13. ⇒ (x + 1/x) = √13. Value of (1) = x² + 1/x² = 11 and (2) = x + 1/x = √13.

If x⁴+1/x⁴ =119, find x²+1/x² and x +1/xPlease answer the question with explanation

Answer»

⇒ If x⁴ + 1/x⁴ = 119.

As we know that,

⇒ (x² + 1/x²)² = x⁴ + 1/x⁴ + 2(x²)(1/x²).

⇒ (x² + 1/x²)² = x⁴ + 1/x⁴ + 2.

Put the value of (x⁴ + 1/x⁴) = 119 in EQUATION, we get.

⇒ (x² + 1/x²)² = 119 + 2.

⇒ (x² + 1/x²)² = 121.

⇒ (x² + 1/x²) = √121.

⇒ (x² + 1/x²) = 11.

As we know that,

⇒ (X + 1/x)² = x² + 1/x² + 2(x)(1/x).

⇒ (x + 1/x)² = x² + 1/x² + 2.

Put the value of (x² + 1/x²) = 11 in equation, we get.

⇒ (x + 1/x)² = 11 + 2.

⇒ (x + 1/x)² = 13.

⇒ (x + 1/x) = √13.