Question

x-1divided by x is 5 find x vube - 1 by x cube using idneities?

Answer 1

Given

• (x - 1/x) = 5

To find

• x³ - 1/x³

Solution

◐ (a-b)³ = a³-b³-3ab(a-b) ◐

➛ a = x ➛ b = 1/x

• (x - 1/x)³ = x³ - 1/x³ - [3×x×1/x×(x-1/x)]
• (5)³ = x³ - 1/x³ - (3×5)
• 125 = x³ - 1/x³ - 15
• x³ - 1/x³ = 125 + 15
• x³ - 1/x³ = 140

∴ x³ - 1/x³ = 140