Question

If x²+1/x²=3 then find the value of (x⁶+1/x³)²​

Answer 1

$\huge\mathsf\purple{Answer}:-$

Given Equation is x² + (1/x²) = 7.

It can be written as,

⇒ x² + (1/x²) = 9 - 2

⇒ x² + (1/x²) + 2 = 9

⇒ (x + 1/x)² = 9

⇒ x + 1/x = 3.

On cubing both sides, we get

⇒ (x + 1/x)³ = (3)³

⇒ x³ + 1/x³ + 3(x + 1/x) = 27

⇒ x³ + 1/x³ + 3(3) = 27

⇒ x³ + 1/x³ + 9 = 27

⇒ x³ + 1/x³ = 18.

plz mark me as brainliest

Answer 2

Step-by-step explanation:

Given Equation is x² + (1/x²) = 7.

It can be written as,

⇒ x² + (1/x²) = 9 - 2

⇒ x² + (1/x²) + 2 = 9

⇒ (x + 1/x)² = 9

⇒ x + 1/x = 3.

On cubing both sides, we get

⇒ (x + 1/x)³ = (3)³

⇒ x³ + 1/x³ + 3(x + 1/x) = 27

⇒ x³ + 1/x³ + 3(3) = 27

⇒ x³ + 1/x³ + 9 = 27

⇒ x³ + 1/x³ = 18.