Question

x⁴+1uponx⁴= 119 find the value of x³-/1/x³​

Answer 1

Answer:

36

Step-by-step explanation:

x⁴ + 1/x⁴ = 119

x⁴ + 1/x⁴ + 2= 121

(x²)² + 2.x²× 1/x² + (1/x²)² = 11²

x² + 1/x² = 11 [Ignoring the negative as LHS is positive]

Now, again the same.

x² + 1/x² - 2 = 9

(x - 1/x)² = 3²

x - 1/x = +3 or -3

Taking cube on both sides,

(x - 1/x)³ = (+-3)³

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

x³ -1/x³ - 3(x - 1/x) = 3³

x³ - 1/x³ - 3 × 3 = 27

or x³ - 1/x³ - 3 × -3 = -27

x³ - 1/x³ = 27 + 9 = 36

or x³ - 1/x³ = 27 + 9 = -36