Question

hey .....mates please answer my question...

if a + 1 /a =6 & a is not equal to zero then find
1)a- 1/a
2)a ^2 -1 / a ^2

Answer :
1)+- 4√2
2)+- 24√2

how is it .....
please tell answer step by step



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Answer 1

Solution:

Given : a + 1/a = 6 & a ≠ 0

Find the value of a + 1/a ?

( a + 1/a)² - ( a - 1/a)² = 4

⇒ ( 6 )² - ( a - 1/a)² = 4

⇒ 36 - ( a - 1/a)² = 4

⇒ ( a - 1/a)² = 36 - 4

⇒ ( a - 1/a)² = 32

⇒ a - 1/a = √32

⇒ a - 1/a = 4√2

• ∵ a - 1/a = 4√2

Find the value of a - 1/a ?

( a + 1/a)( a - 1/a) = a² - 1/a²

⇒ (6)( 4√2) = a² - 1/a²

⇒ a² - 1/a² = 24√2

• ∵ a² - 1/a² = 24√2

Answer 2

Answer:

1). a - 1/a = ± 4√2

2). a² - 1/a² = ± 24√2

Step-by-step explanation:

1)

Solve:

Given,

a + 1/a = 6

where a is not equal to 0.

Solve,

(a + 1/a)² - (a - 1/a)² = 4

=> (6)² - (a - 1/a)² = 4

=> 36 - (a - 1/a)² = 4

=> (a - 1/a)² = 36 - 4

=> (a - 1/a)² = 32

=> a - 1/a = √32

=> a - 1/a = ± 4√2

.°. a - 1/a = ± 4√2

2)

Solve:

(a + 1/a) (a - 1/a) = a² - 1/a²

=> (6) × (4√2) = a² - 1/a²

=> a² - 1/a² = ± 24√2

.°. a² - 1/a² = ± 24√2