Question

Find the value of x³ + 1/x³, if x² + 1/x² =14 ​

Answer 1

52

Explanation:

• x² + 1/x² = 14

(x+1/x)² -2 = 14

(x+1/x)²= 16

x+1/x = √ 16 =4

∴ x+1/x = 4

• x³+1/x³= (x+1/x)³

(x+1/x)³= x³ + 1/x³ + 3 × x × 1/x (x + 1/x) (cubic Identity)

(x+1/x)³ = x³ +1/x³+ 3(4)

(4)³=x³+1/x³+12

64-12=x³+1/x³

• 54=x³+1/x³

Answer 2

Explanation:

x² + 1/x² = 14

(x + 1/x)² -2.x.1/x = 14

(x + 1/x )² -2 = 14

(x + 1/x )² = 16

take square root both sides

(x + 1/x) = 4

then,

[a³+b³=(a+b)³-3ab(a+b)]

x³ + 1/x³ = ( x + 1/x)³ - 3.x.1/x(x + 1/x)

= ( x +1/x)³ -3(x + 1/x)

= (4)³ -3(4)

= 64 - 12

= 52