Question

If a-(1/a) = 5 , how do I find the value of a³-(1/a³)-200=?

Answer 1

Answer:

Well, the problem gives you the value of a−1a , and you want to find a3−1a3 . We can get an expression involving a3 and 1a3 if we cube both sides of a−1a=5 .

If we do this, we get (a−1a)3=a3−3a+3a−1a3=125 .

Well, that’s better. We can pull out the parts of that equation that we want to get a3−1a3=125+3a−3a .

We already know the value of 125, so we just need to find the value of 3a−3a . Wait a minute! That’s just 3 times a−1a , which is 5! (the number 5, not 5 factorial)

Thus, a3−1a3=125+3a−3a=125+3⋅5=140