Question

If a-1/a = 5, then what is the value of a³-1/a³?​

Answer 1

Answer:

If a-1/a = 5 . then, [a -1/a]^3 = (5)^3 a^3 - 1/a^3 - 3a×1/a(a - 1/a) = 125 a^3 -1/ a^3 -3(5) = 125. (putting the value of a -1/a)

Step-by-step explanation:

nice

Answer 2

Answer:

Basic theory comes with binomial expression. As you know

(a+b)3=a3+3a2b+3ab2+b3

also

(a−b)3=a3−3a2b+3ab2−b3

In this case

(a−1a)=a3−3a21a+3a1a2−1a3=53=125

By simplification and take required parts to close, we can obtain a eq”,

(a3−1a3)−3(a−1a)=125

Then we can substitute the values to suitable places.

(a3−1a3)−(3×5)=125

(a3−1a3)=125+(3×5)=140

I think the real problem has the printing mistake. The ans” should be 140. Not 400.

HERE IS THE ANOTHER METHOD TO SOLVE THIS…

We know that (a3−b3)=(a−b)(a2+ab+b2)

(a−1a)2=a2−2+1a2=52=25

(a−1a)=a2+1a2=27

In our problem. It can be express to following form.

(a3−1a3)=(a−1a)(a2+1+1a2)

Substitute the values what we obtain…

(a3−1a3)=5×(27+1)=5×28=140