Question

help karo plzzz


if [a²+(1/a²)]=23
than find [a²-(1/a²)]​​

Answer 1

Answer:

5√21

See the attachment.

Answer 2

to complete the square on LHS , we add

2*(a^2)*(1/a^2) on both sides .

a^2 + 1/a^2 + 2(a^2)*(1/a^2) = 23 + 2(a^2)*(1/a^2)

( a + 1/a )^2 = 23 + 2

(a + 1/a)^2 = 25

taking square root on both sides.

(a+1/a) = √25

a + 1/a = 5 ------( 1)

now ,

we add -2*(a^2)*(1/a^2) on both sides .

a^2 + 1/a^2 - 2*a* 1/a^2 = 23 - 2(a^2)(1/a^2)

(a - 1/a)^2 = 23 -2

(a - 1/a)^2 = 21

a - 1/a = √21 --------(2)

so as we know , A^2 - B^2 = (A+B)(A-B)

,

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

from 1 & 2

= (5) * (√21) = 5√21