Question

solve question no 10

Answer 1

10.

Given a + 1/a = 6.

On Squaring both sides, we get

(a + 1/a)^2 = (6)^2

a^2 + 1/a^2 + 2 * a * 1/a = 36

a^2 + 1/a^2 + 2 = 36

a^2 + 1/a^2 = 36 - 2

a^2 + 1/a^2 = 34


(i) Now,

Let a - 1/a = x.

On Squaring both sides, we get

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

a^2 + 1/a^2 - 2 * a * 1/a = x^2

34 - 2 = x^2

32 = x^2

$x = \sqrt{32}$


(or) 

(a + 1/a)^2 = (a - 1/a)^2 + 4

(6)^2 = (a - 1/a)^2 + 4

36 = (a - 1/a)^2 + 4

32 = (a - 1/a)^2

$a - \frac{1}{a} = \sqrt{32}$




(ii)

$a^2 - \frac{1}{a^2} = (a + \frac{1}{a} )(a - \frac{1}{a})$

                                    $= 6 * \sqrt{32}$

                                    $= 6 \sqrt{32}$


Hope this helps!

Answer 2

hey!!

here is your answer >>>>>>>

=> a + 1/a = 6!


Let us whole square this equation!

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

as we know, a+1/a is 6.. , let's substitute!

(6)^2 = a^2 + (1/a)^2 + 2

a^2 + 1/(a)^2 is 36-2

=> 34!

Now, let's find a-1/a,

let us square this!

we get,

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

we know that,

a^2 + 1/(a)^2 is 34!

(a-1/a)^2 = 34-2

= √32

this can be written as

√4 * √4 * √2

=>> 2*2*√2

=>> 4√2 is the answer


hope this helps!