Question

if x+1/x=3 then find value of x3+1/x3and x2+1/x2

Answer 1

Use formula (x+y)^3
And (x+y)^2

Answer 2

Answer :

x³ + 1 / x³ = 18

x² + 1 / x² = 7

Step-by-step explanation :

x + 1 / x = 3

On cubing both the sides ;

⇒ ( 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 = 27 - 9

⇒ x³ + 1 / x³ = 18

Hence, x³ + 1 / x³ = 18

Again,

x + 1 / x = 3

On squaring both sides ;

( x + 1 / x )² = ( 3 )²

⇒x² + 1 / x² + 2 = 9

⇒x² + 1 / x² = 9 - 2

⇒x² + 1 / x² = 7

Hence, x² + 1 / x² = 7