Question

If x square+1/x square=7 find the value of x cube +1/x cube , taking only the positive value of x+1/x

Answer 1

Answer:

x³ + 1/x³ = 18

Step-by-step explanation:

x² + 1/x² = 7

On adding 2 both sides ;

x² + 1/x² + 2 = 7 + 2

⇒ ( x + 1/x )² = 9

⇒ x + 1/x = √9

⇒ x + 1/x = ±3

So, taking the positive value.

x + 1 / x = 3

On cubing both sides ;

( x + 1/x )³ = (3)³

⇒ x³ + 1/x³ + 3 * x * 1/x (x + 1/x) = 27

⇒ x³ + 1/x³ + 3 (3) = 27

⇒ x³ + 1/x³ + 9 = 27

⇒ x³ + 1/x³ = 27 - 9

⇒ x³ + 1/x³ = 18

Hence, the value of x³ + 1/x³ is 18.

Answer 2

Answer:

x² + 1/x² =7

(x + 1/x)² - 2(x/x) = 7

(x + 1/x)² = 9

x + 1/x = 3

(x + 1/x)³ = 3³

x³ + 1/x³ + 3 x/x (x + 1/x) = 27

x³ + 1/x³ = 27 - 9

x³ + 1/x³ = 18

hope its helpful................