Question

If x square plus 1 upon x square=7. Find
the value of x cube plus 1 upon x cube.​

Answer 1

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x³ + 1/x³ = 18

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Answer 2

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.