Question

Simplify - 3/2a² (a²-1) + 1/4a² (a²+a) - 3/4a(a³-1) ​

Answer 1

Answer:

What is the answer when a-(1/a) =2, then a³-2a²-(2/a²)-(1/a³) =?

We are trying to find a3−2a2−2a2−1a3 given that a−1a=2 .

Some quick manipulation before we start that will help:

First, a−1a=2

Next,

(a−1a)2

=a2−2(a)(1a)+1a2

=a2+1a2−2

Another way of expressing the expression squared is (a−1a)2=22=4

So a2+1a2=6 . Remember this.

And:

(a−1a)3

=a3−3(a2)(1a)+3(a)(1a2)−1a3

=a3−3a+3a−1a3

=a3−3(a−1a)−1a3

=a3−1a3−6

Similarly , we can also say that (a−1a)3=23=8 .

So (a−1a)3=14

With that, our solution becomes easier.

a3−2a2−2a2−1a3

=(a3−1a3)−2(a2+1a2)

=14−2(6)

=2

Answer 2

Step-by-step explanation:

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