Question

10. If a + 1/a = 6 and a unequal to 0
then find
1) a - 1/a
2) a² - 1/a²​

Answer 1

Given:

• a+1/a = 6.

To Find:

• The value of

1. a - 1/a
2. a² - 1/a²

Answer:

Now here we are given that , a+1/a=6.

=> a + 1/a = 6.

=> ( a + 1/a)² = 6².

=> a² + 1/a² + 2×a×1/a = 36.

=> a² + 1/a² + 2 = 36.

=> a² + 1/a² = 36-2.

=> a² + 1/a² = 34 .

We will be now using it to find other two required values.

=> a² + 1/a² - 2×a×1/a = 34-2×a×1/a.

=> (a - 1/a )² = 34 - 2.

=> a - 1/a = √32.

=> a - 1/a = 2√5.

Now we know that (a+b)(a-b) = a²-b²

=> (a² - 1/a² ) = ( a + 1/a ) ( a - 1/a )

=> a² - 1/a² = 6 × 2√5

=> a² - 1/a = 12√5.