Question

if X square + 1 divided by x square is equal to 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

as we know that (a + b)² = a² + b² + 2ab

using a = x and b = 1/x

(x + 1/x)² = x² + 1/x² + 2

putting value of x² + 1/x² = 7

=> (x + 1/x)² = 7 + 2

=> (x + 1/x)² = 9

=> (x + 1/x)² = (±3)²

=> x + 1/x = ±3  

=> x + 1/x = 3   as only positive value to take

x³ + 1/x³

a³ + b³ = (a+b)³ -3ab(a+b)

= (x + 1/x)³ - 3(x + 1/x)

= 3³ - 3(3)

= 27 - 9

= 18

so

x³ + 1/x³ = 18