Question

If a -1/4 =4 then prove that a^3 - 1/a^3 =76

Answer 1

Step-by-step explanation:

I believe your Question is,

"If (a - (1/a)) = 4, then prove that, (a³ - (1/a³)) = 76

We have,

(a - (1/a)) = 4

Now,

We know that,

(a - b)³ = a³ - 3ab(a - b) - b³

So, using the identity,

(a - (1/a))³ = 4³

a³ - 3(a)(1/a)(a - (1/a)) - (1/a)³

Here,

a × (1/a) = 1 [ a cancels out]

a - (1/a) = 4 [Given]

So,

a³ - 3(4) - (1³/a³) = 64

a³ - 12 - (1/a³) = 64

a³ - (1/a³) = 64 + 12

a³ - (1/a³) = 76

Hence proved

Hope it helped and believing you understood it........All the best.