188k views
0 votes
A + 1 / a = 4 Find (a+1/a)³​

Pls solve this

2 Answers

3 votes

Answer:

(a + 1/a)^3 = A^3 + 13.75.

Explanation:

To solve this problem, we first need to simplify the expression (a + 1/a)^3 using the identity (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.


Let's start by expanding (a + 1/a)^3:(a + 1/a)^3 = a^3 + 3a^2(1/a) + 3a(1/a)^2 + (1/a)^3


We can simplify this expression using the fact that 1/a^2 = 1/a * 1/a:


(a + 1/a)^3 = a^3 + 3a + 3/a + 1/a^3


Now, we can substitute the given equation A + 1/a = 4:


(a + 1/a)^3 = A^3 + 3A + 3(1/A) + 1/a^3


We still need to find the value of a^3 + 1/a^3. To do this, we can use the identity a^3 + b^3 = (a + b)(a^2 - ab + b^2), where a = a and b = 1/a:


a^3 + (1/a)^3 = (a + 1/a)(a^2 - a(1/a) + (1/a)^2)


a^3 + (1/a)^3 = (a + 1/a)(a^2 - 1 + 1/a^2)


But we know that A + 1/a = 4, so A^2 + 1/a^2 = (A + 1/a)^2 - 2 = 4^2 - 2 = 14. Substituting this in the previous expression gives:


a^3 + (1/a)^3 = (4)(14 - 1) = 52


Finally, substituting in the expression we derived earlier for (a + 1/a)^3 gives:


(a + 1/a)^3 = A^3 + 3A + 3(1/A) + 52

We know that A + 1/a = 4, so substituting this gives:


(a + 1/a)^3 = A^3 + 3(4) + 3(1/4) + 52 = A^3 + 13.75


Therefore, (a + 1/a)^3 = A^3 + 13.75.

User Faklyasgy
by
8.2k points
0 votes

Answer:

If a+1/a=4, then (a+1/a)^3=4^3, and 4^3=4x4x4=64

User Carbonr
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories