Question

X^2 + 1/X^2 = 98 then X^3 + 1/X^3 = ?

Answer 1

Solution:

Given ,

x² + (1/x²) = 98

Adding 2 on both the sides

→ x² + 1/x² + 2 = 98 + 2

→ x² + 1/x² + 2(1) = 100

Here ,

One can be written as x(1/x)

→ x² + 1/x² + 2[x(1/x)] = 100

It is in the form of

• a² + b² + 2ab = (a + b)²

Similarly

→ [x + (1/x)]² = 100

→ x + 1/x = √100

→ x + 1/x = 10 …….… ( i )

Now , cubing on both sides

→ (x + 1/x)³ = 10³

Using

• (a + b)³ = a³ + b³ + 3ab(a + b)

Similarly

→ x³ + 1/x³ + 3x(1/x)[x + 1/x] = 1000

→ x³ + 1/x³ + 3[x + 1/x] = 1000

Using equation 1

→ x³ + 1/x³ + 3(10) = 1000

→ x³ + 1/x³ = 1000 - 30

→ x³ + 1/x³ = 970.. [ Answer ]