Question

Guys pleqse solve this question.
It's urgent.

The best and the correct answer will be marked as Brainliest.

Q. 47

Answer 1

Given : a^4 + (1/a^4) = 727.

It can be written as,

⇒ a^4 + (1/a^4) = 729 - 2

⇒ a^4 + (1/a^4) + 2 = 729

⇒ (a^2)^2 + (1/a^2)^2 + 2(a^2)(1/a^2) = 729

⇒ (a^2 + 1/a^2)^2 = 729

⇒ a^2 + 1/a^2 = 27.

Now, It can be written as

⇒ a^2 + (1/a^2) = 25 + 2

⇒ a^2 + (1/a^2) - 2 = 25

⇒ (a - 1/a)^2 = 25

⇒ a - 1/a = 5.

On cubing both sides, we get

⇒ (a - 1/a)^3 = (5)^3

⇒ a^3 - 1/a^3 - 3(a - 1/a)= 125

⇒ a^3 - 1/a^3 - 3(5) = 125

⇒ a^3 - 1/a^3 - 15 = 125

⇒ a^3 - 1/a^3 = 140.

Hope this helps!