Question

if x-1/x = 3+2√2,find the value of x3-1/x3​

Answer 1

Answer:

x-1/x = 3+2√2,

(x)³-(1/x)³=(3)³+(2√2)³

x³-1/x³=9+16√3

Answer 2

Answer:-

Given:

x - 1/x = 3 + 2√2 -- equation (1)

Cubing both sides we get,

⟹ (x - 1/x)³ = (3 + 2√2)²

using -

• (a - b)³ = a³ - b³ - 3ab(a - b)

• (a + b)³ = a³ + b³ + 3ab(a + b)

we get,

⟹ (x)³ - (1/x)³ - 3 * x * 1/x (x - 1/x) = (3)³ + (2√2)³ + 3 * 3 * 2√2 (3 + 2√2)

Putting the value of x - 1/x in LHS we get,

⟹ x³ - 1/x³ - 3(3 + 2√2) = 27 + 16√2 +

18√2(3 + 2√2)

⟹ x³ - 1/x³ - 9 - 6√2 = 27 + 16√2 + 54√2 + 72

⟹ x³ - 1/x³ = 99 + 70√2 + 6√2 + 9

⟹ x³ - 1/x³ = 76√2 + 108

∴ The value of x³ - 1/x³ is 76√2 + 108.