Question

If a - 1/a = 3 then a2 - 1/a2

Answer 1

Step-by-step explanation:

a - 1/a = 3 (given)

a^2 - 1/a^2 = ?

we can solve this problem by applying the formula of (a-b)^2 which is equal to a^2 + b^2 - 2ab, here a = a and b = 1/a,

applying the formula,

(a-1/a)^2 = a^2 + 1/a^2 - 2 × a × 1/a

(3)^2 = a^2 + 1/a^2 - 2

11 = a^2 + a^2 + 1/a^2

now we have to find the value of (a+1/a), by applying (a + b)^2 = a^2 + b^2 + 2ab , we can do it.

(a + 1/a)^2 = a^2 + 1/a^2 + 2 × a×1/a

(a+1/a)^2 = 11 + 2

(a + 1/a)^2 = 13

(a+1/a) = √13

now in last step we will applying the formula of (a^2 - b^2) which is equal to = (a+b) (a-b)

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

= √13 × 3

= 3√13

It is a very easy question dear first we found the value of (a^2 + 1/a^2) from (a-1/a) from that value of (a^2 + 1/a^2) we found the value of (a+1/a) and then we equate (a^2 - 1/a^2) . hope it helps.