If (x² + 1/x²) = 98, find the value of x³ + 1/x³.

We know that: (x + y)² = x² + y² + 2xy

Replace y with 1/x, we get

(x + 1/x)² = x² + 1/x² + 2

Since (x² + 1/x²) = 98 (given)

(x + 1/x)² = 98 + 2 = 100

or (x + 1/x) = ±10

Now, Find x³ + 1/x³

We know that, x³ + y³ = (x + y)(x² + y² – xy)

Replace y with 1/x, we get

x³ + 1/x³ = (x + 1/x)(x² + 1/x² – 1)

Use (x + 1/x) = 10 and (x² + 1/x²) = 98

x³ + 1/x³ = 10 x 97 = 970

x³ + 1/x³ = 970