Question

solve
please fast please please​

Answer 1

Answer:

a + ( 1 / a ) = 3

a - ( 1 / a ) = √5

a ^ 2 - ( 1 / a ^ 2 ) = 3√5

Step-by-step explanation:

Solution,

We have,

a ^ 2 + ( 1 / a ^ 2 ) = 7

{a + ( 1 / a) }^ 2 - 2 . a . ( 1 / a ) = 7       (∵  (a + b) ^ 2 – 2ab)

{a + ( 1 / a) }^ 2 - 2 = 7

{a + ( 1 / a) }^ 2 = 7 + 2

{a + ( 1 / a) }^ 2 = 9

{a + ( 1 / a) }^ 2 = (3) ^ 2

a + ( 1 / a ) = 3

Again,

a ^ 2 + ( 1 / a ^ 2 ) = 7

{a - ( 1 / a) }^ 2 + 2 . a . ( 1 / a ) = 7       (∵  (a - b) ^ 2 + 2ab)

{a - ( 1 / a) }^ 2 + 2 = 7

{a - ( 1 / a) }^ 2 = 7 - 2

{a - ( 1 / a) }^ 2 = 5

{a - ( 1 / a) }^ 2 = (5) ^ 1 / 2

a - ( 1 / a ) = √5

Now,

a ^ 2 - ( 1 / a ^ 2 ) = { a + (1 / a)}{ a - (1 / a)}

                            = 3 * √5

                            = 3√5

Answer 2

a + ( 1 / a ) = 3

a - ( 1 / a ) = √5

a ^ 2 - ( 1 / a ^ 2 ) = 3√5

Step-by-step explanation:

Solution,

We have,

a ^ 2 + ( 1 / a ^ 2 ) = 7

{a + ( 1 / a) }^ 2 - 2 . a . ( 1 / a ) = 7       (∵  (a + b) ^ 2 – 2ab)

{a + ( 1 / a) }^ 2 - 2 = 7

{a + ( 1 / a) }^ 2 = 7 + 2

{a + ( 1 / a) }^ 2 = 9

{a + ( 1 / a) }^ 2 = (3) ^ 2

a + ( 1 / a ) = 3

Again,

a ^ 2 + ( 1 / a ^ 2 ) = 7

{a - ( 1 / a) }^ 2 + 2 . a . ( 1 / a ) = 7       (∵  (a - b) ^ 2 + 2ab)

{a - ( 1 / a) }^ 2 + 2 = 7

{a - ( 1 / a) }^ 2 = 7 - 2

{a - ( 1 / a) }^ 2 = 5

{a - ( 1 / a) }^ 2 = (5) ^ 1 / 2

a - ( 1 / a ) = √5

Now,

a ^ 2 - ( 1 / a ^ 2 ) = { a + (1 / a)}{ a - (1 / a)}

                            = 3 * √5

                            = 3√5