Question

Q3. If a² + 1/a² =18

Find (i) a -1/a (ii) a³ +1/a³
please solve this question ASAP​

Answer 1

Answer:

4

Step-by-step explanation:

Given,

a²+1/a²=18

To find the value of -

i) a-1/a

Solution

i) a-1/a

Here we need to convert a²+1/a² into negative to get the solution

So,

a²+1/a²=18(Given)

=>a²+1/a²-2×a×1/a+2×a×1/a=18

Here a²+1/a² is in identity 1 (a+b)². So to make it negative (a-1/a)² that is the formula of identity 2 (a-b)² we included -2×a×1/a and +2×a×1/a.

=>(a-1/a)²+2×a×1/a=18

In identity 2 we know (a-b)²=a²-2ab+b². So in this case we did the opposite one i.e. we included -2×a×1/a to a²+1/a²-2×a×1/a to make it (a-1/a)². And that +2×a×1/a is the formula of identity 1 that we put again and brought to right side.

=>(a-1/a)²=18-2

=>(a-1/a)²=16

=>a-1/a=Square root of 16

=>a-1/a=4

So, a - 1/a is 4.

Hope this has helped you