Question

If x^2 + 1/x^2 = 98, find the value of x^3 + 1/x^3 = ?​

Answer 1

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Answer 2

• Question : If x² + 1/ x² = 98, find the value of x³ + 1/x³ = ?

x² + 1/x² = 98

x² + 1/x² = 100 - 2

x² + 1/x² + 2 = 100

We know that,

[(x + 1/x)² = x² + 1/x² + 2]

.°. (x + 1/x)² = 10²

Square rooting both sides,

x + 1/x = 10

Now, Again,

Cubing both the sides,

(x + 1/x)³ = 10³

x³ + 1/x³ + (3 × x ×1/x) × (x + 1/x) = 1000

x³ + 1/x³ + 3 × 10 = 1000

x³ + 1/x³ = 1000 – 30

= 970

• Thus, 970 is the required answer.